> 



£*f 




\ LIBRARY OF CONGRESS. 



BCiog" 
-^ . JD4- 

w UNITED STATES OF AMERICA. 




% 



Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/elementsoflogicc01dayh 



ELEMENTS OF LOGIC, 



COMPRISING 



THE DOCTRINE OF THE LAWS AND PRODUCTS OF 

THOUGHT, AND THE DOCTRINE OF METHOD, 

TOGETHER WITH A LOGICAL PRAXIS. 



DESIGNED EOR CLASSES AND EOR PRIVATE STUDY. 



BY 



HENRY N. DAY, 

AUTHOR OF "ART OF RHETORIC," "RHETORICAL PRAXIS," ETC. 



Nam neque decipitur ratio, nee decipit unquam. 

The mixture of those things by speech, which by nature are divided, is the mother 
of all error. 



NEW YORK: 
CHARLES SCRIBNEE AND COMPANY. 

1867. 






Entered according to Act of Congress, in the year 1867, by 

Henry N. Day, 

In the Clerk's Office of the District Court for the District of Connecticut. 



RIVERSIDE, CAMBRIDGE: 

STEREOTYPED AND PRINTED BT 

H. 0. HOUGHTON AND COMPANY. 



PREFACE 



The present work is designed for learners. As a branch 
of science, the study of Logic commends itself by very 
special, not to say preeminent claims to all lovers of learn- 
ing and liberal culture. But a leading motive in the prepa- 
ration of this volume has been to furnish a needed help to the 
training of thought for effective communication in discourse. 
The first requisite for good speaking and good writing is 
the power to think well ; and to a good thinker, the study 
of Logic as the science of Thought bears the same rela- 
tion as the study of mathematics to a good civil engineer. 

The plan of the work has been determined by this 
governing design. The aim has been to develop the science 
in strict method. From the determination of the single 
radical principle of Thought, its Laws and the forms of 
its Products have been methodically evolved ; and the Doc- 
trine of Method with the Exercises is but the end and 
result toward which the unfolding of the Doctrine of the 
Elements of Thought has steadily tended. The barbarous 
terminology of the Scholastic Logic, shown by Sir Wil- 
liam Hamilton to be as erroneous as useless, is discarded, 
except so far as seemed necessary for understanding the 
forms in which it has entered and modified general liter- 
ature. The Exercises are prepared for the help of the 
teacher, rath or than to be used just as they are presented, 



IV PREFACE. 

except, perhaps, in small classes, where free conversational 
discussion and criticism are practicable, and in private 
study. For large classes there may be found necessary 
special adaptations of the material here furnished, which 
may be used to suggest other exercises or to furnish op- 
portunity of ready selection. 

The hope that this object of training for effective think- 
ing, and especially with reference to the construction of 
Discourse, may be better accomplished than through other 
published treatises on Logic, has been one principal induce- 
ment to prepare the present work. But some new things 
will be found to characterize it, which, if approved and 
accepted as valuable contributions to the advancement of 
the science, may, of themselves, justify this address to the 
public. 

These contributions are in part to be found in the fol- 
lowing particulars, to which the attention of the cultivators 
of the science is particularly solicited. 

1. The rigid reduction of Thought to its one essential 
principle — that of Identity. 

2. The unfolding of the Laws and of the forms of the 
Products of Thought under this principle, and the validat- 
ing of each of them by it. 

3. The formal derivation of the Concept and of the 
Eeasoning from the primitive product, of Thought — the 
Judgment — under the principle regulative of all Thought 
— that of Identity. 

4. The determination of the reciprocal relations and dis- 
tinguishing characteristics of Concepts in respect of their 
peculiar Quantities, and of the relations of Concepts to Lan- 
guage. 



PREFACE. V 

5. The more exact discrimination of the Thought-process 
itself from its object-matter or datum. 

6. The determination of the different kinds of Wholes 
in which Thought may proceed, and the discrimination of 
those founded in the matter or datum to Thought from 
those which are the pure product of Thought itself. 

7. The full development of the relationship of Part to 
Complementary Part as one of the two relationships in 
which all Thought proceeds, equally primitive and neces- 
sary with that of Whole to Part ; this last being the only 
one recognized hitherto by logicians, who have, by unavoid- 
able consequence, been obliged to give a one-sided and 
therefore essentially imperfect and unsatisfactory develop- 
ment of the whole science, and either to exclude the con- 
sideration of Inductive Reasoning altogether or to give an 
entirely erroneous and pernicious presentation of it. 

8. The formal grounding of all Induction, so far as a 
process of Thought, on this relationship of Part to Comple- 
mentary Part, with a full unfolding of its laws, its forms, 
and its uses. 

9. The more exact exposition of Logical Disjunction, of 
the grounds of distinction between Contradictory and Con- 
trary Oppositions, of Modality and its distinctions, and of 
Necessary and Contingent Truth. 

10. A new classification of Reasonings, — the logical con- 
sequence of modifications of logical doctrine already indi- 
cated. 

11. A new system of Logical Methodology, more pre- 
cisely defined as the Doctrine of the Conditions of Thought 
in order to perfect science. 

12. A Logical Praxis, comprising copious exercises sep- 






VI PREFACE. 



arately arranged for each of the forms of the various prod- 



ucts of Thought, 



A free use has been made of the elaborations of Sir 
William Hamilton, who, however defective and imperfect 
his system appears in his posthumous lectures, has done 
more for the science, it may perhaps be said without ex- 
travagance, than all that has been done for it since the 
times of Aristotle. In some cases, where his language 
has been used, it has been modified and changed to make 
his teachings correspond to those that are peculiar to the 
present work. These borrowings are indicated by the usual 
quotation marks without more special reference, and with- 
out any discrimination of Hamilton's free borrowings from 
German writers, or of the changes made in his statements. 
The intended uses of the book as a text-book seemed to 
forbid the incumbering of the text with such special refer- 
ences, while this general acknowledgment will enable any 
critical reader to ascertain the extent to which these bor- 
rowings have been carried. 



New Haven, Conn., November, 1866. 



CONTENTS. 



INTRODUCTION. 

PAGE 

§ 1. Definition of Logic 1 

§2. Its Utility: — a. Objective; I. Subjective . . 3-12 
§ 3-6. Its Divisions 12-16 



PART I. 

THE ELEMENTS OF THOUGHT. 

CHAPTER I. 

THE NATURE OF THOUGHT. 

§ 7. Elements of Thought: — 1. Laws; 2. Products . 17 

§8. Thought a relative Cognition 17-19 

§9. Nomenclature of Attributes . . . . . 19,20 

CHAPTER II. 

THE LAWS OF THOUGHT. 

§ 10-14. The Four Laws of Thought : — 1. Of Identity ; 
2. Of Contradiction ; 3. Of Disjunction ; 4. Of 
Exclusion 21-25 

§ 15. Quantity in all Thought . . . . . 25, 26 

CHAPTER in. 

THE WHOLES IN THOUGHT. LOGICAL POSTULATE. 

§ 16, 17. Kinds of Wholes . . . . . . 27-29 

§ 18. Hamilton's Postulate 29, 30 



viii CONTENTS. 

CHAPTER IV. 

THE PRODUCTS OF THOUGHT. — I. JUDGMENTS. 

PAGB 

§ 19, 20. Judgment defined and explained . . . 31-35 
§ 21, 22. Terms :— Subject; Predicate . . . 35-38 

§ 23. The Copula 38, 39 

§ 24. Division of Judgments 39-47 

§ 25, 26. — 1. As to Quality : — Affirmative ; Negative ; 

Disjunctive 48-51 

§ 27. — 2. As to Modality : — Assertory ; Problematic ; 

Apodictic 51, 52 

§ 28. — 3. As to Degree of Identity : — Identical ; Par- 
tial ; Tautological . . . . 52, 53 
§ 29, 30. — 4. As to Character of Terms : — Categor- 
ical; Hypothetical; Hypothetico-Disjunct- 

ive . 53-56 

§ 31. — 5. As to Logical Quantity : — Extensive ; Inten- 
sive 56, 57 

§ 32. — 6. As to Kind of Whole : —Integrate ; Substan- 
tial ; Causal 57,58 

§ 33. Judgments in relation to one another . . . 58-61 

CHAPTER Y. 

THE PRODUCTS OF THOUGHT. — II. CONCEPTS. 

§ 34-38. Formation and Essential Nature of Concepts 62-65 
§ 39. Relations to Objects and to Language . . . 65-72 
§ 40-44. Quantity of Concepts : — Extensive and In- 
tensive . 72-78 

§ 45-50. Relations of Concepts in Extension . . 78-86 

§51-54. Relations of Concepts in Comprehension . 86-90 

CHAPTER VI. 

THE PRODUCTS OF THOUGHT. — III. REASONINGS. 

§ 55-58. Nature, Denominations, and Divisions of Rea- 
sonings . 91-94 

§ 59-65. Immediate Reasonings : — Conversion ; Quan- 
titative Restriction ; Modal Restriction ; 
Transference; Disjunction; Composition 94-102 



CONTENTS. IX 

PAGE 

§66-70. Categorical Syllogisms : — Deductive; Induc- 
tive 102-118 

§ 71-77. Conditional Syllogisms : — Ponent and Tol- 
lent ; Hypothetical; Dilemma ; Disjunct- 
ive . . . . . . . . 118-128 

§78-80. Polysyllogism : — Epichirema ; Sorites . . 128-131 

PART II. 

METHODOLOGY. 

CHAPTER I. 

METHOD IN GENERAL. 

§81. Nature of Method 132,133 

§ 82-87. Threefold Perfection of Science : — Material ; 

Formal; Verbal 133-146 

CHAPTER II. 

METHOD IN SPECIAL. — METHODOLOGY OF JUDGMENTS. 

§ 88. The Three Conditions of Perfection in Judgments 147-149 
§89-95. Special Rules of Judgments . . . 149-156 

CHAPTER III. 

METHODOLOGY OF CONCEPTS. 

§ 96. The Three Conditions of Perfection in Concepts . 157 

§97. Objective Law of Concepts 157-163 

§ 98-108. Subjective Law : — Logical Definition ; 

Analysis 163-180 

§ 109. Verbal Law . 180-182 

CHAPTER IV. 

METHODOLOGY OF BEASONINGS, 

§110. Probation and Investigation . 183,184 

§111. Objective Law of Reasonings .... 184,185 
§112-124. Subjective Law 185-206 



X CONTENTS. 

PAET III. 

LOGICAL PRAXIS. 

PAGB 

I. Exercises in Judgments . • . . 207-214 

II. Exercises in Concepts 214 

III. Exercises in Reasonings 214-222 

Appendix A. Induction 223-227 

" B. Origin of Language . . • ,227-231 



INTRODUCTION. 



DEFINITION OF LOGIC. 

§ 1. Logic is the Science of the Laws of Logic de _ 
Thought as Thought. fined - 

The name, Logic, is derived from Aoyos, which word in 
Greek had a twofold meaning, denoting both thought 0rigia of 
and the expression of thought. To avoid the Name - 
ambiguity thus arising, Aristotle limits the term, when ap- 
plied to thought, by the definitive rbv eo-w — that within the 
mind ; and when applied to the expression of thought, — to 
speech, by the definitive rbv efoo — that without. 

It has been a point much discussed whether Logic is a 
science, or an art, or neither, or both. " Plato and L ic a gci _ 
the Platonists received it as a science ; but with ence * 
them Dialectic was coextensive with the Logic and Metaphys- 
ics of the Peripatetics taken together. By Aristotle himself, 
Logic is not defined. The Greek Aristotelians, and many 
philosophers since the revival of letters, deny it to be either 
science or art. The Stofcs, in general, view r ed it as a science ; 
and the same was done by the Arabian and Latin schoolmen. 
In more modern times, however, many Aristotelians, all the 
Pamists, and a majority of the Cartesians, maintained it to 
be an art ; but a considerable party were found who defined 
it as both art and science. In Germany, since the time of 
Leibnitz, Logic has been almost universally regarded as a 
science." 

By a science, is meant only a branch of knowledge, un- 
1 



2 INTRODUCTION. 

folded in systematic method. It would seem superfluous to 
attempt a formal vindication of the claims of Logic to be 
thus regarded. 

The object-matter of Logic is Thought, strictly so called, 
its Object- as tne product of the Discursive Faculty, other- 
Matter. w j se ca u ec [ the Faculty of Comparison, the Under- 
standing, and by Hamilton, the Elaborative Faculty. This 
term, thought, has been used to include any act of conscious- 
ness, whether a cognition, a feeling, or a volition. It has 
been more commonly used to include any act of the Intelli- 
gence — any cognitive act. But as the object-matter of 
Logic, it is used in a still more restricted meaning to denote 
only an act of the Discursive Faculty — the Faculty of 
mediate cognition. Logic, accordingly, takes no account of 
the faculties of original cognition — the Presentative Facul- 
ties of Perception, Self- Consciousness, and Intuition ; nor of 
the Faculties of Representative Knowledge — Memory and 
Imagination. The range of Thought proper, then, is far 
more limited than the bounds of the Intelligence, as a de- 
partment of mental activity coordinate with the feelings and 
the will. And of the several Faculties of the Intelligence, 
it is restricted to the operations of but one — the Discursive 
Faculty, or Faculty of Comparison. 

The distinctive nature of Thought may be indicated in a 
general way thus : The Faculties of original cognition first, 
as a condition to the exercise of Thought, present to the 
mind one or another of their several objects. These objects, 
as apprehended, become, as cognitions, the materials upon 
which the Faculty of Thought then commences its opera- 
tions. If, for example, the Faculty of Perception present 
any object, as a Tree, the object is first apprehended 
vaguely and simply by itself. But as the attention is con- 
centrated upon it, it is apprehended as standing in certain 
relations — either in external relations to other objects which 
with it make up a certain sphere of knowledge to us, or in 
internal relations to some of its own parts or properties. 



INTRODUCTION. 3 

The object, thus viewed in relation to the object without or 
to the part or property within, is said to be thought. Before, 
the tree was simply perceived — known simply in itself; now 
it is known relatively to something else — to some object ex- 
ternal to itself, or to some internal part of itself: for instance, 
externally, as distant from some other external object ; or, 
internally, as broadly-branched, as covered with foliage, as 
fruit-bearing, or as having some other property or character. 
Thought, then, is a cognition, not immediate and irrelative, 
as is a perception, an intuition, an imagination, but mediate 
and relative — a cognition of an object as related to some- 
thing else. We think the tree, when we apprehend it as dis- 
tant, as branching, and the like — as having some attribute. 

Logic, thus, as the science of Thought, is limited to a single 
department of our cognitive functions — to the function of 
relative cognitions. Its more precise nature will be exhibited 
in the sequel. 

§ 2. The utility of Logical Science may be estimated 
from the inherent excellence and interest of the utility of 
Science itself, and from its value as a Mental Dis- L ° S1C " 
cipline and Instrument of Knowledge. 

Objectively, as a science to be acquired and understood, 
Logic claims a twofold consideration. First, in ( a ) object- 
respect of its object-matter, Human Thought, s^rice of As 
no science presents more commanding induce- Thou s ht - 
ments to its investigation and study. The mechanism of 
Thought, its parts, its springs, its movements, its products, its 
guides and principles, — no subject certainly possesses a prior 
claim to the consideration of Thought itself than this its own 
mechanism. All science, all our systematic, methodical know- 
ing, is the product of Thought. Thought introduces into the 
Temple of Truth. The first truth we gain is given us by 
Thought, and all subsequent truth is equally her gift. Per- 
ception and Self-Consciousness give us objects of knowledge, 
furnish the rude materials of Thought. But their products 
are, in themselves, but the most meagre, vaguest cognitions. 



4 INTRODUCTION. 

They are only impressions. It is the prerogative of Thought 
to attribute to these vague impressions reality, to determine 
their relations to the universe of truth around, to mark the 
inner properties which characterize and qualify them. 

It is under the prompting and guidance of Thought, indeed, 
that Perception itself moves on from the most indeterminate 
observations to full and definite cognitions. Without the aid 
of Thought, it stumbles and falls at the very threshold of 
knowledge. The keenest eye and the most laborious delving 
in the earth can at best uncover but little of the story of the 
antediluvian world. Out of a single fragment of a fossil, 
geological Thought reads a voluminous history of life, habits, 
conditions, laws, belonging to ages before the flood. The 
mere observer might sweep his eye over volumes of an an- 
cient language, and be little wiser as to its history and con- 
nections, its laws and structure ; while a single page fur- 
nishes all the conditions necessary to enable the disciplined 
Thought of the philologist to determine all. The great part 
of astronomical facts, of such as are attainable without 
Thought, were known to the early Oriental shepherds. 
Thought, out of those few observations, has constructed that 
magnificent structure of modern astronomy. Indeed, human 
Intelligence would be little elevated and expanded above and 
beyond that of the brute without the Faculty of Thought. 
By the comparative excellence of the object-matter of Log- 
ical Science may we, thus, estimate its own importance and 
value. 

But Logic presents another peculiar attraction, as a Pure 
2. As Pure Science. Its matter lies in the mind itself; and 
Science. ft treats only of that which is necessary in that 

matter. It has this feature in common with Mathematical 
Science. They both found themselves upon the operations 
of the same faculty — the Discursive Faculty, which, if 
viewed in its essential characteristics, and exclusively of its 
conditions and accessories, is simply an identifying faculty, 
ever and only recognizing the same and the different. In 



INTRODUCTION. 5 

Mathematical Science, its identities are those which are 
found only in the forms in which Being enters into our ex- 
perience — the forms of Space, and Time, and are only those 
of the equal, the more and the less, in magnitude and number. 
In Logical Science, the identities in Being itself, as it comes 
into our experience, — the same and the different there, are 
in addition brought into view. Now, as only what trans- 
pires within its own realm can be accepted by Thought as 
strictly necessary, as what is given to thought must be ever 
taken only as given, — must be assumed, and so viewed as 
only problematical — all necessary matter lies in thought ; and 
as Logic, like Mathematics, takes into view only the neces- 
sary in thought itself, it is, as conversant only with the 
necessary, a Pure Science. Mathematics and Logic are, 
thus, as the only sciences of pure thought, the only sciences 
of necessary truth. No other science possesses properly the 
character of necessary matter, except so far as pure thought 
enters into and characterizes it ; and wherever, in whatever 
department of knowledge, pure thought enters, there is ne- 
cessary truth. There is here discovered an eminent inci- 
dental utility of Logical Science that it enables us to discrim- 
inate readily what is necessary from what is at best but 
contingent in any department of knowledge, while it claims 
to itself all those distinctive attractions and excellencies 
which properly belong to Pure Science. 

Subjectively, however, as Instrument of Knowledge and 
of Mental Discipline, Logic claims the highest con- (t>) Subject- 

., ' . ^ c ' .° & ive Utility 

sideration as a useful science. of Logic. 

It is, indeed, in a certain restricted sense, only a Formal 
Instrument of Knowledge. It can of itself effect no new dis- 
covery in the field of matter from which it derives the con- 
ditions of its operations. We cannot begin with our thought, 
and out of that evolve being — construct sciences of the world 
external to thought. It is but gross self-imposture to assume 
a mere form of thought, an empty formula, and then, out of 
this, educe outward, objective reality. It is no function of 



6 INTRODUCTION. 

Thought, of itself to amplify any science in respect to the 
proper object-matter of that science. So far as it attempts 
this, it invades the territory of the Presentative Faculties, 
and its attempts are suicidal. . • 

Still, Logic is true Instrument of Knowledge. It prompts 

1. As Aid to an( l guides the proper Presentative Faculties. 
Discovery. Except as these lead on to Thought, and except 
as Thought elaborates their rude and indeterminate cogni- 
tions, they themselves seem to lose spring and motive to 
exertion. They are, to a great extent at least, blind, also, 
and need to be directed as to the proper objects which they 
are to apprehend and to present to Thought. How much of 
modern astronomical discovery has been prompted and guided 
by Thought ? Certain relations in the solar system, obtained 
by pure, scientific Thought, indicated the existence of plan- 
etary worlds here or there in space ; and the telescope, guided 
by these indications of Thought, brought the unknown worlds 
into view. Indeed, a large proportion of the new discoveries 
that are made in the progress of every science have origi- 
nated in what have been vaguely called analogies, which have 
been furnished by Thought. And it is the province of Logic 
to unfold the laws that govern these analogies, determine 
their conditions, test their soundness and validity. 

Further, all proper science is the product of Thought, and 

2. As Builder lies wholly within the domain of the Discursive 
of Science. F acu i ty f fl^ human Intelligence. The cogni- 
tions of Perception, as already remarked, are vague and in- 
definite ; the cognitions of the pure Reason, or, as it has been 
called, the Regulative Faculty, are equally without limita- 
tion and without relation. Science is relative and defined 
cognition. It is the proper province of Logic to acquaint us 
with the laws of all science, or all relative cognition, and thus, 
in the intelligent application of these laws, to conduct us to 
assured knowledge. 

While Thought deals only with cognitions, with what is 
already in the mind, and thus, strictly speaking, originates 



INTRODUCTION. 7 

no material knowledge, we must not take in too narrow an 
application the truth that it is but the Formal Instrument 
of Knowledge. Mathematics, like Logic, is a Formal Sci- 
ence, yet our knowledge of the heavenly bodies has been 
chiefly furnished to us by Mathematics. The facts given in 
observation are comparatively meagre. Astronomy has in 
fact made most of its growth since the time of Kepler and 
Newton, and that growth has been effected chiefly by math- 
ematicians, not by observers. What Mathematics is to the 
outer world, Logic is to the inner world of truth. Neither 
can do anything for any object of science, till the object is 
given to it ; neither can start forth and from its own unde- 
rived and unacquired resources construct any system of 
knowledge. But matter being given it in very meagre 
amounts, and each, in its sphere, can build up vast struct- 
ures of true knowledge ; for the essential qualities of any 
object of knowledge are very few in comparison with the 
relative. While the observed attributes increase arithmet- 
ically, the relations of thought increase with the rate of per- 
mutation and combination. When a fragment of a bone was 
presented to Cuvier, he was enabled in thought to read in it 
the size, age, habits, the specific characteristics of the animal 
to which it belonged. So Thought, out of a fragment of 
fact, interprets rich and vast treasures of truth through its 
relations, internal and external. It is true that Logic is not 
Thought ; it is true, also, that men think without Logic. So 
Mathematics is not Astronomy ; and men can compute without 
arithmetical rules. But how extremely limited is all such 
computation, all such thought ; and at best how uncertain are 
its results, and even although correct, how little assurance 
do these results give to the ignorant calculator and thinker ? 
The absolute impotence of Logic, of Thought, to construct 
a science in any department, without the matter of that sci- 
ence being previously given in experience, is now every 
where recognized. Not so distinctly recognized is its de- 
pendence on the other faculty or source of knowledge — the 



8 INTRODUCTION. 

Regulative Faculty — the Reason — Common Sense. But 
if not its absolute impotence, still its impotence to any thing 
valuable or worthy, is just as real without the ideas of the 
Reason, as without the facts of experience. Of what worth 
would science be to us, even were it possible, that proceeded 
independently of our ideas of Space and Time ; of Being, 
Substance, Cause ; of Truth, Beauty, Rectitude, and Good- 
ness ? Logic can venture forth not one step in safety, or in 
promise of attaining any worthy result, except as these great 
ideas of the Reason guide and animate, as its processes are 
upon and through these fundamental data of the Intelligence. 
But in turn, these grand ideas are of little worth to us, ex- 
cept as Thought apprehends them, scans them in their mani- 
fold relations, and then determines and indicates these rela- 
tions. 

Logic, indeed, is not Thought ; it is only Thought applied 
to Thought ; the science of Thought, or still more precisely, 
the science of the necessary in Thought. But this very lim- 
itation of Logic suggests its immeasurable utility to the spirit 
of man, whose dignity consists so much in Thought. If 
Logic is not Thought, it yet presides over Thought, and pre- 
scribes its function and its sphere. It preserves us, thus, 
from illusions and phantoms, which are for the most part 
occasioned by the confounding of experiences and thoughts ; 
and the consequent imposition of thoughts for objects. 

Logic, moreover, opens the way for Thought, and by pre- 
senting occasions, calls it forth into exercise. It teaches 
how it may fasten upon an object of experience, or an idea 
of the Reason ; trace out its relations ; determine its proper- 
ties, its conditions, its bearings. The chief obstacle to think- 
ing is ignorance how to think. Matter enough is given in 
every outlook upon the external world, in every glance 
turned inward upon our mental experience, to provoke and 
to sustain endless thought. Thought does not go forth as 
this gate of occasion opens to it, because it does not see. 
Logic opens its eyes upon the relations in their diversity, 
through which it may go forth to its work. 



INTRODUCTION. 9 

Logic, further, completes and perfects Thought. Thought 
necessarily remains feeble and immature, except as it is 
developed and matured by Logic. As Mathematics enables 
Thought to carry its computations to indefinite limits, and 
to pace off the measureless skies, while the savage can only 
compute but several scores, and can measure only where the 
foot can tread ; so Logic not only carries Thought forward in 
every particular direction to its remotest bounds, but also 
carries it over the entire field of its explorations, so that no 
part shall be overlooked. 

Logic is useful, also, in correcting our knowledge. It has 
been justly termed a medicine of the mind, as it 3. as Correc- 
helps to purge it from errors which impair and tive of Error, 
vitiate its healthful activity. It does not directly heal the 
imperfection or error that may have crept into its opera- 
tions at the original presentation of its matter. But when, 
by its sure procedure, it discovers that the original datum 
as presented to it has led to results that are not in har- 
mony with its already ascertained truths, or that involve 
contradictory relations, or that do not admit of being per- 
fectly brought under the complete and necessary conditions 
of thought, by detecting the fact of error and its probable 
source, it guides and helps to the needful correction by the 
proper presentative faculty; precisely as Mathematics, al- 
though like Logic a purely formal science, can show that 
there is error somewhere in the original measurement, or the 
running of the lines of a survey, if the bearings and distances 
as given will not admit of being plotted into a bounded field, 
and may indicate also, possibly, where the error originated, 
so that it may be corrected by new survey. 

Logic, still further, is of eminent utility in furnishing the 
proper assurance of Truth. If it is much to know, 4 Ag as _ 
it is often more to know that we know ; to be rea- surin s truth - 
sonably assured that what we accept as true is indeed true, as 
verified by the only possible criteria of truth within the reach 
of the human mind. Confidence in the correctness of the 



10 INTRODUCTION. 

procedures of Thought, confidence in the validity of the re- 
sults of Thought, is one of the leading conditions of success 
in all thinking. To be in doubt whether we are on the road 
to truth, whether we are in possession of the requisite means 
of attaining it, whether what we at last have reached is the 
truth we seek, is very mental imbecility. It is the preroga- 
tive and proper function of Logic, as the Science of the Laws 
of Thought, to remove the grounds of such doubt, to indicate 
and so to assure as certain the way to truth, and to impart 
credibility to the results of Thought. It is true that, in large 
departments of our knowledge, what we know can have at 
best but the character of probable truth, never that of abso- 
lute certainty. But it is the part of Logic to point out just 
where the lines that separate probable from absolute certainty 
run, and also to discover just where the contingency in im- 
perfect knowledge attaches ; the nature, the source, the ex- 
tent, the means, if any, of removal of all that impairs our 
knowledge. Such is the assurance that Logic gives to our 
thinking. 

" But it is not only by affording knowledge and skill that 
6. As in- Logic is thus useful ; it is perhaps equally con- 
Se°UndCT- ducive to the same end by bestowing power. The 
standing. retortion of thought upon itself — the thinking of 
thought — is a vigorous effort, and, consequently, an invigor- 
ating exercise of the Understanding ; and as the Understand- 
ing is the instrument of all scientific, of all philosophical specu- 
lation, Logic, by preeminently cultivating the understanding, 
in this respect likewise vindicates its ancient title to be viewed 
as the best preparatory discipline for Philosophy and the 
sciences at large. 

" But Logic is further useful as affording a Nomenclature 
6. As af- °f tne l aws D y which legitimate thinking is gov- 
en r tmc Sa No-~ erne< ^? an( l °f tne violations of these laws, through 
menciature. w hich thought becomes vicious or null. 

" Words do not give thoughts ; but without words, thoughts 
could not be fixed, limited, and expressed. They are, there- 



IISTTRODUCTION. 11 

fore, in general, the essential condition of all thinking worthy 
of the name. Now, what is true of human thought in gen- 
eral, is true of Logic and Rhetoric in particular. The no- 
menclature in these sciences is the nomenclature of certain 
general analyses and distinctions, which express to the initi- 
ated, in a single word, what the uninitiated could (supposing, 
what is not probable, that he could perform the relative proc- 
esses) neither understand nor express without a tedious and 
vague periphrasis ; while, in his hands, it would assume only 
the appearance of a particular observation, instead of a par- 
ticular instance of a general and acknowledged rule. To 
take a very simple example : there is in Logic a certain 
sophism, or act of illegal inference, by which two things are, 
perhaps in a very concealed and circuitous manner, made to 
prove each other. Now, the man unacquainted with Logic 
may perhaps detect and be convinced of the fallacy ; but how 
will he expose it ? He must enter upon a long statement and 
explanation, and after much labor to himself and others he 
probably does not make his objection clear and demonstrative 
after all. But between those acquainted with Logic the 
whole matter would be settled in two words. It would be 
enough to say and show that the inference in question in- 
volved a circle, and the refutation is at once understood and 
admitted. It is in like manner that one lawyer will express 
to another the ratio decidendi of a case in a single technical 
expression ; while their clients will only perplex themselves 
and others in their attempts to set forth the merits of their 
cause. Now, if Logic did nothing more than establish a cer- 
tain number of decided and decisive rules in reasoning, and 
afford us brief and precise expressions by which to bring par- 
ticular cases under these general rules, it would confer on 
all who in any way employ their intellect — that is, on the 
cultivators of every human science — the most important ob- 
ligation. For it is only in the possession of such established 
rules, and of such a technical nomenclature, that we can ac- 
complish, with facility, and to an adequate extent, a criticism 



12 INTRODUCTION. 

of any work of reasoning. Logical language is thus, to the 
general reasoner, what the notation of Arithmetic, and still 
more of Algebra, is to the mathematician. Both enable us 
to comprehend and express, in a few significant symbols, what 
would otherwise overpower by their complexity ; and thus it 
is that nothing would contribute more to facilitate and extend 
the faculty of thinking, than a general acquaintance with the 
rules and language of Logic." 

§ 3. Logic may be divided on different principles of divis- 
Divisions of lon i nto different sets of species, of which the 
Logic. more important are the three following : 

„ « . . First, in reference to the mind or thinking sub- 

1. Object- 7 . rv 

iveandSub- ject, Logic is divided into Objective (Logica Sys- 
tematica) and Subjective (Logica Habitualis). 

" By Objective or Systematic Logic is meant that comple- 
ment of doctrines of which the science of Logic is made up ; 
by Subjective or Habitual Logic is meant the speculative 
knowledge of these doctrines which any individual, as Soc- 
rates, Plato, Aristotle, may possess, and the practical dex- 
terity with which he is able to apply them. 

" Now, it is evident that both these Logics, or rather, Logic 
considered in this twofold relation, ought to be proposed to 
himself by an academical instructor. We must, therefore, 
neglect neither. Logic considered as a system of rules, is 
only valuable as a mean toward Logic considered as a habit 
of the mind ; and, therefore, a logical instructor ought to do 
what in him lies to induce his pupils, by logical exercise, to 
digest what is presented to them as an objective system into 
a subjective habit. Logic in both these relations belongs to 
us, and neither can be neglected without compromising the 
utility of the study. 

§ 4. " In the second place, by relation to its application or 
2. Abstract non-application to objects, Logic is divided into 
2nd concrete Abstract or General, and into Concrete or Spe- 

or Special. cial. 

" Abstract Logic considers the laws of thought as potentially 



INTRODUCTION. 13 

applicable to the objects of all arts and sciences, but as not 
actually applied to those of any ; Concrete Logic considers 
these laws in their actual and immediate application to the 
object-matter of this or that particular science. The former 
of these is one, and alone belongs to philosophy, whereas the 
latter is as multiform as the arts and sciences to which it is 
relative. 

" This division of Logic does not remount to Aristotle, but 
it is found in his most ancient commentator, Alexander the 
Aphrodisian, and, after him, in most of the other Greek 
Logicians. Alexander illustrates the opposition of the logic 
divorced from things, to the logic applied to things, by a 
simile. " The former," he says, " may be resembled to a 
geometrical figure, say a triangle, when considered abstractly 
and in itself; whereas the latter may be resembled to the 
same triangle, as concretely existing in this or that partic- 
ular matter : for a triangle considered in itself is ever one 
and the same ; but viewed in relation to its matter, it varies 
according to the variety of that matter ; for it is different as 
it is of silver, gold, lead — as it is of wood, of stone, etc. 
The same holds good of Logic. General or Abstract Logic 
is always one and the same ; but as applied to this or to that 
object of consideration, it appears multiform.' So far Alex- 
ander. This appearance of multiformity, however, is not 
real ; for the mind has truly only one mode of thinking, one 
mode of reasoning, one mode of conducting itself in the 
investigation of truth, whatever may be the object on which 
it exercises itself. Logic may, therefore, be again well com- 
pared to the authority of a universal empire — of an em- 
pire governing the world by common law r s. In such a 
dominion there are many provinces, various regions, and 
different prefectures. There is one praefect in Asia, another 
in Europe, a third in Africa, and each is decorated by differ- 
ent titles ; but each governs and is governed by the common 
laws of the empire confided to his administration. The 
nature of General Logic may likewise be illustrated by 



14 INTRODUCTION. 

another comparison. The Thames, for instance, in passing 
London, is a single river — is one water — but is there ap- 
plied to many and different uses. It is employed for drink- 
ing, for cooking, for brewing, for washing, for irrigation, for 
navigation, etc. In like manner, Logic in itself is one : as a 
science or an art, it is single ; but in its applications, it is of 
various and multiform use in the various branches of knowl- 
edge, conversant be it with necessary, or be it with contin- 
gent matter. Or further, to take the example of a cognate 
science, if any one were to lay down different grammars of a 
tongue, as that may be applied to the different purposes of 
life, he would be justly derided by all grammarians, indeed 
by all men ; for who is there so ignorant as not to know that 
there is but one grammar of the same language in all its 
various applications ? 

" Thus, likewise, there is only one method of reasoning, 
which all the sciences indifferently employ ; and although men 
are severally occupied in different pursuits, and although one 
is, therefore, entitled a Theologian, another a Jurist, a third a 
Physician, and so on, each employs the same processes, and 
is governed by the same laws, of thought. Logic itself is, 
therefore, widely different from the use — the application of 
Logic. For Logic is astricted to no determinate matter, but 
is extended to all that is the object of reason and intelligence. 
The use of Logic, on the contrary, although potentially ap- 
plicable to every matter, is always actually manifested by 
special reference to some one. In point of fact, Logic, in its 
particular applications, no longer remains logic, but becomes 
part and parcel of the art or science in which it is applied. 
Thus Logic, applied to the objects of geometry, is nothing 
else than Geometry ; Logic, applied to the objects of physics, 
nothing else than Natural Philosophy. We have, indeed, 
certain treatises of Logic in reference to different sciences, 
which may be viewed as something more than these sciences 
themselves. For example : we have treatises on Legal 
Logic, etc. ; but such treatises are only introductions — only 



INTRODUCTION. 15 

methodologies of the art or science to which they relate. 
For such special logics only exhibit the mode in which a 
determinate matter or object of science, the knowledge of 
which is presupposed, must be treated, the conditions which 
regulate the certainty of inferences in that matter, and the 
methods by which our knowledge of it may be constructed 
into a scientific whole. Special Logic is thus not a single 
discipline, not the science of the universal laws of thought, 
but a congeries of disciplines, as numerous as there are 
special sciences in which it may be applied. Abstract or 
General Logic, on the contrary, in virtue of its universal 
character, can only and alone be one ; and can exclusively 
pretend to the dignity of an independent science. This, 
therefore, likewise exclusively concerns us. 

§ 5. "In the third place, considered by reference to the 
circumstances under which it can come into exer- 3. Pure and 
cise by us, Logic is divided into Pure and Modi- Modified - 
fied. Pure Logic considers the laws of thought proper, as 
contained a priori in the nature of pure intelligence itself. 
Modified Logic exhibits these laws as modified in their act- 
ual applications by certain general circumstances external 
and internal, contingent in themselves, but by which hu- 
man thought is always more or less influenced in its mani- 
festations. 

" Pure Logic considers Thought Proper simply and in it- 
self, and apart from the various circumstances by 
which it may be anected in its actual application. 
Human thought, it is evident, is not exerted except by men 
and individual men. By men, thought is not exerted out of 
connection with the other constituents of their intellectual 
and moral character, and, in each individual, this character 
is variously modified by various contingent conditions of 
different original genius, and of different circumstances con- 
tributing to develop different faculties and habits. Now, 
there may be conceived a science which considers Mod jfi e( i 
thought not merely as determined by its necessary Logic * 



16 INTRODUCTION. 

and universal laws, but as contingently affected by the empir- 
ical conditions under which thought is actually exerted ; 
which shows what these conditions are, how they impede, 
and, in general, modify, the act of thinking ; and how, in 
fine, their influence may be counteracted. This science is 
Modified or Concrete Logic. It is identical with what Kant 
and other philosophers have denominated Applied Logic. 

" Modified Logic, however, is neither an essential part nor 
an independent species of General Logic, but a mere mixt- 
ure of Logic and Psychology, and may, therefore,. be called 
Logical Psychology or Psychological Logic. There is thus 
in truth only one Logic, that is, Pure or Abstract Logic. ,, 

§ 6. Pure Logic may be most conveniently distributed 
Parts of mt0 two parts ; — the one of which shall expound 
pure Logic, fas conditions of thinking in itself, irrespectively 
of the proper end of thinking ; the other shall set forth the 
conditions of thinking in order to the attainment of truth or 
science, as the proper end of all thinking. In the first part, 
accordingly, should be exhibited the elements of thought in 
itself, the Absolute Conditions of Thought ; and in the second 
part, the elements of thought in its relations to Truth or 
Science, the Relative Conditions of Thought. 

Pure Logic, then, will embrace the two parts of — 

I. The Doctrine of the Essential Elements of Thought ; 
and, 

II. The Doctrine of Method or Methodology. 

To these two Parts of Systematic Logic should be added 
another of Subjective Logic, in the form of a Logical 
Praxis. 



PURE LOGIC. 

PAET I. 

THE ELEMENTS OF THOUGHT. 

— c — 

CHAPTER I. 

THE NATURE OF THOUGHT. 

§ 7. The First Part of Logical Doctrine embraces the 
Doctrine of the Elements of Thought. These Elements con- 
sist of the necessary Conditions of Thought, and the Prod- 
ucts of Thought. This first part of Logic accordingly com- 
prehends two leading departments, treating severally — 

I. Of the Laws of Thought ; 

II. Of the Products of Thought. 

In order, however, to the more exact determination of the 
nature and validity of these Laws of Thought, and of the 
characters and relationships of these Products of Thought, it 
will be necessary to define, more precisely than we have yet 
done, the nature of Thought itself, so far as Logic takes cog- 
nizance of it. 

§ 8. Thought, in its limited import, as denoting the pro- 
duct of the Discursive Intelligence, is a relative Thought a 

. . relative cog- 

COgnitlOn. nition. 

In Perception, the cognition is immediate and independent ; 
the knowledge is of something considered directly and in 
itself. When I see an individual object thus, — say Buceph- 
alus, or Highflyer, — or when I represent him in imagination, 
I have a direct and immediate apprehension of a certain object 
2 






18 PUEE LOGIC. 

in and through itself. There is no relation in such a cogni- 
tion as a mere perception. But such is the nature of the com- 
plex activity of the human mind, and such the connection 
between its several energies, that while the activity is always 
first awakened by a perception, every perception draws on, 
as by a necessity, the exertion of other energies. Thus, when 
I perceive Bucephalus, I at once have awakened in my mind 
the intuitive idea of existence. There are thus present in 
the mind at the same time the two cognitions ; that of Per- 
ception — Bucephalus — and that of Intuition — Existence. 
These two cognitions are accordingly viewed in relation, 
each to the other ; and the recognition of this relation is 
clearly distinguishable from the two prior cognitions. It is 
a new cognition, — a cognition not of Bucephalus by himself, 
not of Existence by itself, but of Bucephalus as existing. 
This is a thought, a judgment; and is manifestly a relative 
cognition or knowledge ; a cognition, not of objects by or in 
themselves, but of objects in relation to each other ; a cogni- 
tion, in fact, of related cognitions, not of related external 
objects. 

The second cognition into relation with which the cognition 
of Bucephalus is thus brought through the restless and di- 
verse energy of the mind, is not, necessarily and always, it 
should be noticed, an Intuitive cognition. It may be another 
Perception ; as, for instance, on perceiving Bucephalus, I 
may also perceive a part or a property belonging to him, as 
that he is four-footed — quadruped. As before, the cognition 
of Existence, so now that of quadruped is brought into rela- 
tion with the cognition of Bucephalus ; and the relative cog- 
nition, the thought of Bucephalus as quadruped comes up in 
the mind. 

It is obvious that thought, as thus a relative cognition — 
a cognition of cognitions related to each other — necessarily 
respects two cognitions, and two only ; inasmuch as, although 
either one may be itself complex, the relation can properly 
subsist between two only. If, in the combinations of thought 



THE NATURE OF THOUGHT. 19 

and in abbreviations of verbal expression, more than two 
factors seem to be brought into relation, they can always be 
reduced t.o two. Thought is, accordingly, ever and essentially 
a cognition of a duality. 

In the instances given, the second cognition in each case is 
one that is internal in relation to the first ; existence and 
quadruped being qualities recognized as belonging to Buceph- 
alus. In these cases, Bucephalus is viewed as a whole, of 
which existence and quadruped are severally parts. But the 
second cognition may be external to the first ; Bucephalus 
being viewed as a part in relation to some other object, as to 
Alexander. The thought then arises, Bucephalus is Alexan- 
der's* The relation recognized in thought between the first 
and second cognitions, which are its objects, may thus be 
either internal or external to the first. But the judgment in 
all cases is a relative cognition ; and the judgment, as will be 
shown hereafter, is the primitive form of thought from which 
the two others, the concept and the reasoning, are derived. 
All thought thus is a relative cognition. 

Still further, it is apparent that, when I think any thing, I 
view it in relation to one only of many other possible cogni- 
tions. I may think Bucephalus as existing, or as four-footed, 
or as Alexander's, and so on indefinitely. There are so many 
different modes of thought. As I cannot think any thing 
without thinking it in some particular mode, that is, in re- 
lation to some attribute, so these modes, possible to thought, 
are of unlimited diversity. 

Logicians have designated these modes by different terms, 
which it will be of convenience to present and explain in 
connection. 

§ 9. " When we think a thing, this is done by conceiving it 
as possessed of certain modes of being, or quali- The var ._ 
ties, and the sum of these qualities constitutes a ous term s by 

, v > / which the 

concept or notion (yorn±a, i.woia, kirivoia, conceptum, modes of 

. \ A ,, , . . , cogitable ex- 

conceptus, notio). As these qualities or modes istence are 
(7rotorr;T€s, qualitates, modi) are only identified esisnate • 



20 PURE LOGIC. 

with the thing by a mental attribution, they are called attri- 
butes (Karrryopov/jLcva, attributa) ; as it is only in or through 
them that we say or enounce aught of a thing, they are 
called predicates, predicables, and predicaments, or categories, 
these words being here used in their more extensive signifi- 
cation (KdTrryopiau, KaTrjyoprjfJiaTa, Karrjyopovjjieva, prcedicata, 
prcedicabilia, prcedicamenta ) ; as it is only in and through 
them that we recognize a thing for what it is, they are called 
notes, signs, marks, characters (notce, signa, characteres, dis- 
crimina) ; finally, as it is only in and through them that we 
become aware that a thing is possessed of a peculiar and 
determinate existence, they are called properties, differences, 
determinations (proprietates, determinationes). As conse- 
quent on, or resulting from, the existence of a thing, they 
have likewise obtained the name of consequents (e7ro/x€va, 
consequentia, etc). What in reality has no qualities, has no 
existence in thought — it is a logical nonentity ; hence, e con- 
verso, the scholastic aphorism — non^entis nulla sunt prcedi- 
cata. What, again, has no qualities attributed to it, though 
attributable, is said to be indetermined (dSiopio-rov, indeter- 
minatum) ; it is only a possible object of thought." 



CHAPTER II. 

THE LAWS OP THOUGHT. 

§ 10. The Fundamental Laws of Thought, or the condi- 
tions of the thinkable, are four: 1. The Law of Identity ; 
2. The Law of Contradiction ; 3. The Law of Disjunction ; 
and 4. The Law of Exclusion or Excluded Middle. 

The ground of these Laws is furnished in the essential 
nature of the Discursive Faculty, or the Faculty of Thought. 
The primitive and essential gradation in the operations of 
this faculty is the Judgment. Now an act of Judgment, in 
its positive import, is nothing more nor less than the identifica- 
tion of one object with another. When I affirm or judge, on 
perceiving Bucephalus, that he is, or that he is a quadru- 
ped, I only identify existence in the one case, or the attribute 
of four-footed in the other, with Bucephalus, as a part of the 
characters which make up the whole mental object — Buceph- 
alus. If I should affirm all the attributes which I recognize in 
the perception as belonging to him, the predicate would be 
exactly equivalent to the subject. Such an affirmation would 
be difficult or impossible, however, in the case of an individual 
object, as Bucephalus ; but in relation to the object of thought, 
denoted by the term horse, it is not so difficult, as in the judg- 
ment — horse is a single-hoofed, non-ruminant quadruped. 
In this judgment the terms — that is, the subject, or that of 
which we think, and the predicate, or that w 7 hich we think 
of the subject — are in thought exactly equivalent, the impres- 
sions which they make being precisely identical and indistin- 
guishable. As will be shown hereafter, this judgment may 



22 PURE LOGIC. 

be read or interpreted in two ways : 1. In what is called its 
Comprehensive Quantity, thus : the notion, horse, contains or 
is made up of the three characters, single-hoofed, non-rumi- 
nant, quadruped. 2. In its Extensive Quantity, thus : the 
notion, horse, is the single-hoofed, non-ruminant part of the 
class of animals called quadruped. 

In this example, the two terms, the subject and the pred- 
icate, are completely equivalent or identical. But in the 
more common class of judgments the identity affirmed be- 
tween the terms is not complete or total, but only partial ; as 
when it is affirmed the concept, horse, is single-hoofed. In this 
judgment it is only affirmed that, of the characters which 
make up the notion, horse, one is that of being single-hoofed. 
The identification is as real as before ; but it is only partial, 
only respects one of the plurality of characters embraced in 
the subject. 

The essential nature of a judgment is thus an identification, 
total or partial, between its terms. Hence springs its one 
comprehensive law — that of Identity. The force and im- 
port of this law, is, simply, that every positive judgment, 
to be a judgment, must identify — must affirm an identity be- 
tween its terms. 

From this cursory analytic view of the nature of an act 
of thought we can better proceed to determine more exactly 
the ground, the validity, and the special phases of the Law3 
of Thought, by a view of the manner in which thought 
takes place in the mind. 

The Reason, under its specific law of causality, compels 
us to suppose that mental activity is first awakened by the 
presentation of some object from without as its necessary 
condition. Let us suppose this to be some impression on 
the sense — some sensation occasioning a perception. There 
are involved in this act two elements, a mind perceiving and 
an object perceived. The faculty of Thought, now, from the 
necessities of its nature, as necessarily self-active when the 
proper conditions of its acting are brought to it, recognizes 



THE LAWS OF THOUGHT. 23 

these two terms both as existing and also as different from 
each other. The idea of existence is an idea of the Reason ; a 
necessary, primitive idea. It is, accordingly, brought in the 
mind face to face with each of the two factors in the percep- 
tion — the perceiving subject, and the perceived object. 
Thought now, in the first place, necessarily affirms this idea 
given by the Reason — Existence, both of the perceiving mind 
and of the external object — in other words, identifies each 
of them as existing. In the next place, with an equal neces- 
sity, it affirms that the perceiving mind is not the object per- 
ceived ; in other words, it denies that they are identical. 
This is the necessary negative phase of the thought, as the 
former is the necessary positive phase. They constitute the 
tw r o phases of the first, comprehensive, essential law of 
thought, called from its positive phase, the Law of Identity. 

It is necessarily involved in this act of mind — the act of 
thought, as it has now been regarded — that to recognize the 
perceiving mind and the perceived object as the same in all 
respects, that is, to recognize the different as the same, to 
identify the non-identical, is the very contrary of thought — 
is not thought. In this view is founded the second of the 
Necessary Laws of Thought — the Law of Non- Contradic- 
tion, more commonly called for the sake of brevity, the Law 
of Contradiction. 

Still further, in order that thought may thus identify or 
difference, it is plain there must be assumed as the necessary 
condition of its acting that there is that in the nature of its 
objects which admits of their being thus identified or differ- 
enced in thought. In other words, thought begins with the 
Postulate : Of all possible objects of thought, any two are, in 
respect of each other, either the same or different ; and so 
far as apprehended at all in thought must be apprehended 
either as the one or the other — either as the same or differ- 
ent. This is the third Law of Thought, and is called the 
Law of Disjunction. The negative phase of this law, which 
excludes from thought every other mode of apprehending its 



24 PURE LOGIC. 

objects, constitutes the Fourth Law of Thought, called the 
Law of Exclusion, or Excluded Middle. 

The first two laws are founded immediately in the nature 
of thought ; the last two, in the relation of objects to thought. 
The pairs are related to each other as subjective to object- 
ive ; the two in each pair are related to each other as posi- 
tive to negative. 

§ 11. The First General Law of Thought is the Law of 
The Law Identity, or as it might more adequately be denom- 
of identity. inated) tne £ aw f fa Same and Different. It 

prescribes as the primary condition of all true and valid 
thought that there ever enter into it as its constituents in 
its positive form, the Same, and in its negative form, the 
Different. Its formula is : a = a. 

This fundamental Law of Thought has the characters of 
an Axiom. It validates itself, as it is involved in the nature 
of thought. Its sanction is, that unless obeyed, Thought 
cannot be. 

The application of the law is universal, and of like force 
to each of the several products of thought, but, as will be 
seen, in modes peculiar to each. 

§ 12. The Second General Law of Thought is the Law 
The Law of Contradiction, or, as it may more adequately be 

of Contra- ~ . _ _ ' ' n -kt ri -.• • -r 

diction. denominated, the Law ot JN on- Contradiction. It 

prescribes that the elements which enter into any one 
thought be not thought both as same and as different. Its 
formula is : A is not non-A, or A — A = 0. 

This law is but the negative form of the First, and has 
the same self-evidencing character and universal validity in 
Thought. It has been expressed in the formula : Whatever 
is contradictory is unthinkable. Its sanction is, that unless 
obeyed, Thought is destroyed. Just so far as disregarded, 
just so far as the contradictory creeps into thought, thought 
ceases to be valid — becomes a zero. 

§ 13. The Third General Law of Thought is the Law 
of Disjunction. It prescribes that when two objects are 



THE LAWS OF THOUGHT. 25 

presented to Thought, it recognizes them either as identical 
or as non-identical — as the same or as different. Its for- 
mula is : A either is B or is not B. 

The ground of this law is, as already indicated, in the 
nature of all objects possible to thought. Thought neces- 
sarily moves when the conditions are supplied, and these 
conditions are the presence in the mind of any two objects of 
thought, necessarily assumed in their nature either as same 
or as different. Its sanction is that, unless obeyed, the very 
conditions of thought are disowned, and any act of thought 
is vain and impotent. 

§ 14. The Fourth General Law of Thought is the Law 
of Disjunctive Exclusion, also called Excluded The Law 

w J of Exclu- 

Middle, and more briefly Exclusion. It prescribes sion. 
that no third thing be attempted in thought beyond the iden- 
tical and the non-identical, the same and the different. Its 
formula is : A is not other than B or non-B. A — (B or 
non-B) = 0. 

This law is the prohibitory or negative side of the Law 
of Disjunction. Like that, it is grounded on the essential 
nature of things as possible to thought. Its sanction is that, 
unless obeyed, the Faculty of Thought departs from its 
sphere, and its movements are invalid and illusory. 

The Third and the Fourth Law stand in the same relation 
to each other as the First and the Second, constituting like 
them a Duad composed of two elements, a Positive and a 
Negative. 

• The first Duad, the Laws of Identity and Contradiction, 
indicate the positive or actual characters of all true Thought ; 
they are the Subjective Laws of Thought. The second, 
those of Disjunction and Exclusion, express the predeter- 
mining conditions of all actual thought ; they are the Ob- 
jective Laws of Thought. 

§ 15. From what has been said in respect to the nature 
of thought, it appears that in every thought there Relations 
are two terms or factors ; as when I think Bu- —^^oF 
cephaius as existing, there are the two terms wholes - 



26 PURE LOGIC. 

Bucephalus, and Existing. They are parts of the thought. 
This judgment is thus a Whole in relation to the terms, and 
the terms are complementary to each other. If I think at 
all of any subject, I must think some predicate of it ; so if I 
think of any predicate, I must think some subject. In every 
thought, accordingly, is necessarily the double relationship, 
that of Whole and Parts, and that of Parts which are com- 
plementary of each other — the relation of Quantity. A3 
the thought takes in more subjects or more predicates, be- 
comes more composite, the Quantity becomes increased, and 
the relationships between the parts are multiplied, without, 
however, destroying or obliterating the primitive duality 
which characterizes all thought. Instead of one part being 
exactly complementary of another part, it may be but jointly 
with others so complementary — partly complementary of it. 
All proper thought, however complicated, being essentially 
founded on this one principle of Identity, thus of its own 
nature unfolding itself into all the complications of Quantity, 
or the manifold relations of Whole to all or any one of its 
Parts, and of a Part to any one or more complementary 
Parts, it becomes necessary to present here a summary view 
of the different kinds of Wholes which exact and effective 
thought requires should be readily discriminated. This will 
be done in the next chapter. 



CHAPTER III. 

THE WHOLES IN THOUGHT. — LOGICAL POSTULATE. 

§16. Wholes may first be divided into two genera ~ into 

I. A Whole by itself, (totum per se) ; 

II. A Whole by accident, (totum per accidens). 

I. Of the first kind of Wholes, there are Five ( a ) whole 
Species: byitself '' 

1. The Whole of Thought — the Dianoetic Whole. Every 
thought includes a positive and a negative. If we -^ D ianoetio 
think explicitly A is B, we also think implicitly whole. 

A is not non-B. The two make up the whole of the thought 
in the relation of A to B. 

2. The Whole of the necessary Forms in which Being 
enters into thought — the Integrate or Mathemat- 2. integrate 
ical Whole. This species has two varieties : (1.) ematicai 1 " 
The Numerical, or that of Time. (2.) The Geo- Whole - 
metrical, or that of Space. As applied to Bodies in Time 
and Space, these become respectively Collective and Mass 
Wholes ; a Collective Whole being constituted of parts nu- 
merically different from one another, as a heap of stones, a 
forest of trees ; a Mass Whole being constituted of parts spe- 
cially different from one another, as a gallon of water, a block 
of wood. In this kind of Whole, the Mathematical or Inte- 
gral, the parts lie out of one another, and their relation to 
the Whole is expressed by the preposition of 

3. A Whole of Being — an Essential Whole. This in- 
cludes two species : (1.) A Whole of Substance, s Essen . 
composed of substance and attributes — a Substan- tial Whole - 
tial Whole. (2.) A Whole of Cause, composed of Cause and 



28 PURE LOGIC. 

its Effects — a Causal Whole. Substance and Attribute on the 
one hand, and Cause and Effect on the other, are respective- 
ly complementary of each other in our thought, so that we 
cannot think the one without thinking the other; just as we 
cannot think a positive without thinking a negative in a Dia- 
noetic Whole, or a part of a Mathematical Whole, as the half 
of a number, or the half of a surface, without thinking the 
other half. 

4. A Logical Whole, being the artificial whole of the Dis- 
4 Logical cursive Faculty, embracing the two species of 
whole. x. The Extensive Whole, or the Whole of Extension. 

which is the whole of the objects embraced under a notion, 
2. The Intensive or Comprehensive Whole, or Whole of Com- 
prehension, which is the whole made up of the characters or 
attributes that make up a notion. 

Thus the notion man is regarded as a whole, containing 
two kinds of parts. One kind of parts enbraces such as the 
varieties — Asiatic, African, European, American, or the in- 
dividuals that make up the race. The notion is then said to 
be taken in its Extensive Quantity, or the Quantity of Ex- 
tension. It is an Extensive Whole. The other kind of 
parts includes such as Rational, Animal, Intelligent, Suscep- 
tible, Moral. The notion is then said to be taken in its Com- 
prehensive or Intensive Quantity or the Quantity of Compre- 
hension. It is an Intensive or Comprehensive Whole. 

When a notion is taken in Extensive Quantity, it is said 
to contain its parts under it. As the whole man taken exten- 
sively contains under it the parts Asiatic, African, European, 
American, Socrates, Plato, Demosthenes, Ccesar, &c. Or if 
the part be made the subject, the parts, Asiatic, &c, are con- 
tained under the whole, man. Such parts are called Exten- 
sive Parts. 

When, on the other hand, a notion is taken in Comprehen- 
sive Quantity, it is said to contain its parts in it. Thus, the 
whole, man, taken comprehensively, contains in it the attri- 
butes or characters Rational, Animal, Intelligent, Susceptible, 



THE WHOLES IN THOUGHT. 29 

Moral ; or the characters Rational, &c, are contained in the 
notion, man. Such parts are called Intensive or Comprehen- 
sive Parts. 

This kind of Wholes is called Logical, because they are 
thought Wholes ; that is, they are Wholes constructed by the 
mind for its own convenience and use, and not necessarily 
actual wholes. The mind can construct as many of these 
kinds of Whole as it finds necessary ; and, although its classi- 
fications will be founded on correspondencies in the actual 
world, at least, will not designedly contradict them ; yet they 
are, in number and in kind, determined not by the actual, but 
by the conveniencies of science or knowledge. 

As will appear hereafter, an Extensive Whole is composed 
of the subjects of Judgments, and a Comprehensive Whole of 
the predicates of Judgments. 

5. A Corporate or Representative Whole, called also, and 
more properly a Formal or ^Esthetic Whole, is made 5 Corpor . 
up of the matter and the form in every individual ate Wholes, 
object of imagination, or more exactly, and more comprehen- 
sively, it is a Whole made up of idea, and the matter in which 
the idea is embodied. 

§ 17. II. Wholes by Accident include such as the 
relative Whole of Degree, as, Mankind is made up , b) ^^ 
of the poor and the rich ; of Position, as northern h y Accident. 
and southern ; of Affinity, as parent and child, and the like. 

§ 18. "The only postulate of Logic which requires an 
articulate enouncement, is the demand that before The Logic- 

,,..,., al Postu- 

dealing with a judgment, concept, or reasoning, late. 
expressed in language, its import should be fully understood ; 
in other words, Logic postulates to be allowed to state ex- 
plicitly in language all that is implicitly contained in the 
thought. 

This postulate can not be refused. In point of fact, Logic 
has always proceeded on it, in overtly expressing all the 
steps of the mental process in reasoning — all the proposi- 
tions of a syllogism ; whereas, in common parlance, one at 



30 



PURE LOGIC. 



least of these steps or propositions is usually left unex- 
pressed. This postulate, though a fundamental condition of 
Logic, has not been consistently acted on by logicians in 
their development of the science ; and from this omission 
have arisen much confusion and deficiency and error in our 
present system of Logic. Aristotle, however, states of syl- 
logistic — and, of course, his statement applies to Logic in 
general — that the doctrine of syllogism deals, not with the 
external expression of reasoning in ordinary language, but 
with the internal reasoning of the mind itself." 



CHAPTER IV. 

THE PRODUCTS OF THOUGHT. 1. JUDGMENTS. 

§ 19. The primitive and essential gradation of thought 
we have indicated to be the Judgment. In accordance with 
what has been said, a Judgment may be defined to be a rec- 
ognition of the identity or non-identity between j u a gmen t 
any two objects presented to the Faculty of Thought. defined - 
As expressed in words, a Judgment is called a Proposition, 
or in grammatical nomenclature, a Sentence. 

Besides the Judgment, there are two other products of 
thought, both derivatives from the Judgment. The one is 
the Concept, which is derived from several Judgments by an 
act of Conceiving — taking together, in other words, by an act 
of synthesis. The other is the Reasoning, which is derived 
from one or more Judgments by an act of analysis or sepa- 
ration. As all thought is essentially a movement in Quan- 
tity, and as variations in Quantity can be effected only in the 
one or the other of these two directions, synthesis and anal- 
ysis, the Concept and the Reasoning are the only conceivable 
derivatives from a Judgment, except such as consist only in 
variations of form, that do not affect the identity of the 
thought. 

In explication of this definition of a Judgment, it will be 
necessary simply to recall what has been already said in the 
exposition of the general nature of thought. As w r e have 
seen, a judgment necessarily supposes two objects ; and its 
essential characteristic, as an act of Intelligence, consists in 
this : that it is a cognition of this particular relation of iden- 
tity or non-identity between the two objects. These two 



32 PURE LOGIC. 

objects of a judgment are given to it by some other faculty 
of the Intelligence, as of Perception, Intuition, Memory, or 
by the Discursive Faculty itself, in some previous exercise. 
It may be some object of Perception, as Bucephalus. As 
thus given by the Perceptive Faculty, the cognition is of an 
object by itself, without relation either to other objects or to 
the parts of the object itself. Color is not in the perception 
itself distinguished from figure ; neither color nor figure from 
the position or the time in which it is perceived ; and neither 
of these from the useful qualities of the object. All the per- 
ceptible qualities are given together without distinction in the 
presentation itself of the object. But when thus given, the 
mind at once, and by a kind of necessity of its being as essen- 
tially active and reflective, exerts its activity on it, first, by 
apprehending it as a part of a multiplicity of objects around, 
to each of which it stands in relation, and also, as a whole, 
containing parts in itself. This is the primitive and condi- 
tional gradation in all thought — the apprehension of an 
object as a part or as a whole — in other words, in the rela- 
tion of Quantity. Simultaneously with this, it apprehends 
some other object of thought given to it by Perception, or 
by some other Faculty of the Intelligence, or in some pre- 
vious exercise of the Judgment, and thus comes to view the 
two objects thus given in relation to each other, as the same 
or not the same. Its act then becomes complete ; and a per- 
fected product of thought, a Judgment, is the result. Thus 
the second object may be given in the Perception itself, as 
black, or four-footed, and the Judgment recognizes this color 
or this form as belonging to Bucephalus — that is, as iden- 
tical with one of the parts or characters that make up the 
whole perception. Or the second object may be given by 
the Regulative Faculty, or Faculty of Intuition, as of Being, 
of Space, of Time, or other idea of the proper Reason ; and 
then the Judgment identifies Bucephalus with Existence, with 
some part of Space, of Time ; or in other words, affirms 
Bucephalus to be, to be in such a place, at such a time, and 



JUDGMENTS. 33 

the like. The second object of thought may, in like manner, 
be given to the Judging Faculty by the Memory. We may 
identify Bucephalus as now perceived with the Bucephalus 
perceived yesterday ; with the black color, the four-footed 
figure, before perceived in some other object. 

The essential nature of a Judgment, thus, is seen to be an 
identification of one object with another, either totally or par- 
tially — in some one or in all respects. It is accordingly a 
relative cognition ; and in the relation which it involves are 
necessarily contained three elements: 1. The object of 
thought identified with some other. 2. The object with 
which it is identified, either in whole or in part. And, 3. 
The mental act which identifies. The first two constitute 
the matter of thought, the datum; the last is the Thought 
itself, the identifying cognition — the Judgment. 

§ 20. To the several parts, or to different aspects of 
the complex procedure in* all Thought as thus exemplified in 
one of its gradations — the Judgment — Psychology has as- 
signed distinctive names, which it may not be inexpedient 
here to recall. 

Inasmuch as the original datum or object of thought is 
given in an indefinite vagueness as one and undi- 
vided, and as, in order to be cognized in thought, 
it must be viewed in relation to some part, it becomes neces- 
sary to loosen up, to analyze or separate it as a whole into 
its parts. This part of the process is called Analysis. 

The next step is to select the part out of the whole for sepa- 
rate apprehension, and to draw it away, as it were, to ab- 
stract it from the other parts. This part of the movement 
in Thought is called Abstraction. The term, ho w- 

.. . ,,. t i • • Abstraction. 

ever, it is proper to add, is applied m various ways 
by different writers or on different occasions, but with the 
same result. Thus it may be applied to the mind itself; so 
that in Abstraction the mind, when confining its view to cer- 
tain parts of an object, is regarded as being abstracted or 
drawn away from the parts that are to be excluded from 
3 



34 PURE LOGIC. 

view ; and this, it may be observed, is in strictness the most 
correct view. But in a looser sense the term may be applied 
to the part itself that is selected, and then such part is re- 
garded as being abstracted from the other parts. Or, in the 
third place, it may be applied to those other excluded parts 
themselves, and then they are regarded as being abstracted 
or drawn away either from the other parts or from the mind's 
consideration. The result is the same in any view, that one 
part is separated from the other parts for exclusive consider- 
ation, and it is therefore a matter of indifference, so far as the 
result is concerned, which of these different views is enter- 
tained. 

When thus one part is separated from the rest for exclu- 
sive consideration by the mind, the act of mind in 

Attention. J . . . 

which it concentrates its notice upon it is called 
Attention. 

In the next place, the two objects are brought up and 
viewed face to face with each other in order that their iden- 
tity or non-identity may be apprehended. This part of the 
process is called Comparison. 

Finally, the last part of the complex process, in which the 
thought is perfected by bringing together the two 

Synthesis. * i . |i , J &o& 

objects attended to into one relative cognition, is 
called an act of Synthesis. 

All Thought thus begins with an Analysis, it proceeds by 
Abstraction, Attention, and Comparison, it ends with a Syn- 
thesis. And this is to be understood in a sense more or less 
full and complete, in modes varying with the nature of the 
particular gradation of all the acts of thought, whether in 
judging, conceiving, or reasoning. The two essential elements 
of thought are analysis and synthesis. With one it neces- 
sarily begins, with the other it necessarily ends. For its very 
function is to lead to truth, to a unity in the intelligence, 
which supposes an undistinguished manifold as its condition, 
and a gathering into a unity as its result. The other parts 
of the complex process, abstraction, attention, and compari- 



JUDGMENTS. 35 

son, are the means by which the mind passes from the mul- 
tiform given in the analysis to the unity in the synthesis. 

Inasmuch as in a Judgment an object is regarded only in 
one of manifold relations, the act is appropriately called a 
determination of the object — a limiting down to some speci- 
fied relationship. And, accordingly, the object which is iden- 
tified with another is called the determined element of the 
judgment, and that with which it is identified, is called the 
determining element. 

§ 21. Of the two objects of thought identified in a Judg- 
ment, one is necessarily viewed as the primitive p ar t SO fa 
which is to be identified with the other, or is deter- Jud sment. 
mined by it. This so viewed primitive or determined object 
is called the Subject ; which may be defined to be that of 
which we judge. The other, viewed as the determining ele- 
ment, is called the Predicate, which may be defined to be that 
which is judged of the subject. The Subject and the Predi- 
cate make up the matter of thought or the datum to thought. 
They are called the Terms of a Proposition, {termini, Spot.) 
The act of thought itself which recognizes the identity be- 
tween the two terms is called the Copula, which may be defined 
to be the identification of two objects of thought. It was 
called by Aristotle, in reference to the two terms, an Interval, 
(Siacrn7/xa). 

Thus, in the proposition, iron is magnetic, we have iron 
for the Subject, magnetic for the Predicate, and is for the 
Copula. It is not always the case, however, that in proposi- 
tions the copula is expressed by is, or in a distinct word from 
the predicate. 

In fact the copula is expressed separately thus only when 
the subject is apprehended as substance and the Judgment 
identifies one of its parts as a quality. As in the example, 
iron is magnetic, the meaning is that one of the qualities of 
the subject, iron, is the quality magnetic — iron, in one 
respect, is magnetic, the identification being partial. But in 
the proposition, iron magnetizes, the subject, iron, is appre- 



36 PURE LOGIC. 

hended as cause. In this expression the copula is merged in 
the predicate. In the English Language there are no longer 
verbs expressing simply quality, like, perhaps, the Latin 
albet, rubet, and as in the obsolete English of Wickliffe, " Thou 
maddist." They all express action, and require that the sub- 
ject be apprehended as cause. And the meaning of the 
proposition, iron magnetizes, is that it identifies a part of the 
causal agency of iron with magnetizing. Here, also, the 
identification is partial. There is, perhaps, one exception to 
this general remark in regard to English verbs. The so- 
called substantive verb, to be, is used often to express the 
quality of Existence, as : God is ; there is a God. There 
are manifold other ways of expressing the copula, which 
will, so far as necessary, be indicated hereafter. 

§ 22. The word Term, as used technically in Logic, it 
The Terms should be observed, is applied either to the sub- 
ment. ject or to the predicate of a proposition. It may 

embrace one or more principal notions ; thus in the proposi- 
tion, The greatest vicissitude of things among men is the 
vicissitude of sects, there are three principal notions or 
objects of thought in the subject, vicissitudes, things, men ; 
but with the other modifying and relative words they make 
but one logical Term. So the predicate contains two notions 
or objects of thought. In a single proposition, there can be 
but two Terms — one subject and one predicate. In a com- 
pound proposition there are, of course, as many Terms as 
there are distinct subjects affirmed of, and distinct predicates 
affirmed. In the proposition, James and John are related, 
there is but one affirmation, one subject, one predicate, and, 
accordingly, two Terms. In the proposition, James and John 
are learned and virtuous, there are distinguishable four 
affirmations, four subjects, four predicates, and eight Terms, 
inasmuch as it may be decomposed into the four single prop- 
ositions : Jams is learned, John is learned, James is virtuous, 
John is virtuous. It should be added that the judgment 
may be compounded of two or more copulas. 



JUDGMENTS. 37 

The Terms of a Judgment are ever to be viewed as objects 
of thought. Even when a Term is presented as an original 
primitive datum by another Faculty, as the Perceptive, and 
so far as thus given, affords only a simple, irrelative cogni- 
tion, so soon as it is accepted by the Faculty of Thought, it 
assumes a new character ; it is no longer simple, but a rela- 
tive cognition. Thus in the judgment, Bucephalus is four- 
footed, the subject, Bucephalus, is in the thought appre- 
hended either as an individual — as one of many four-footed 
things ; as a part of a whole — or as a whole containing one 
of many parts, which here are attributes or characters, as 
that of four-footed, that is, as one of many other attributes 
that belong to Bucephalus as a substance. 

As objects of thought, the Terms of a Judgment are thus 
ever cognitions, not real objects. In the Judgment, Buceph- 
alus is four-footed, the subject is Bucephalus, as known, as 
already introduced into the mind by the Perceptive Faculty, 
and entertained there not as actual, but only as known. 
This observation has been made sufficiently prominent, per- 
haps, in the exposition already given of the nature of 
Thought ; but it cannot well be too forcibly impressed on the 
mind, in the study of the elements of thought, that they are 
all cognitions ; and not only that, but they are also all essen- 
tially relative cognitions. A Term, thus, is not a simple 
representation, as Hamilton seems to teach, but a relative 
cognition, partaking at once, as soon as accepted by thought ? 
of the relativeness that is characteristic of all thought. 

The Terms of a judgment may be conveniently distrib- 
uted into three classes, distinguished by the re- Terms of 

. i»ii ii three grades 

spective modes in which they are thought, or or classes. 
more exactly, by the different stages at which they are 
respectively accepted as objects in the elaborative process 
bestowed by thought on the original datum. At the first 
stage is this primitive datum itself, as accepted from the 
Perceptive or Intuitive Faculties, and invested with the 
character of relativeness attaching to all thought; of this 






38 PURE LOGIC. 

class are all individual and simple cognitions, as Bucephalus, 
Mars, Socrates, Space, Time, Being, Identical, and the like. 

At the next stage are the products of a synthesis of these 
terms of the first class, to be hereafter more fully described, 
called Concepts, which, as modified or not, make up the 
larger part of the Terms used in discourse. 

At the third stage are Judgments themselves used as 
Terms in other Judgments ; as, That men are free is a doc- 
trine of general recognition ; If virtue is voluntary, vice is 
voluntary. A Judgment thus used as a Term is called a 
Clause. That men are free, is thus a Clause. 

§ 23. Besides the Terms, — the Subject and the Predi- 
The Copula cate, — as we have seen, there" is another element 
ment. in the Judgment, namely, the Copula, a reciprocal 

relation between these Terms as determining and determined. 
This is the pure Thought-element. It is important here 
to investigate its precise nature or character. We have 
already found that all thought is relative — that it ever 
proceeds under the relations of Quantity. Now there are 
two kinds of relationship, equally primitive and equally 
necessary, involved in this general relation of Whole and 
Parts. There is first the relation of Whole to Part, with 
its converse of Part to Whole. There is next, the relation 
of Part to Part ; as we cannot think a Part without thinking 
its Complementary Part. These two, then, are the primitive 
channels of thought, inasmuch as it moves ever between the 
Whole and the Part, or between the Part and the Complement- 
ary Part. The Copula determines indifferently in either of 
these two relations. It identifies the Whole as containing the 
Part, and identifies one Part as complementary of the other. 
This is its positive form. It denies, however, as well as 
affirms ; it differences as well as identifies. Accordingly in 
one relation it differences in one view the Whole from the 
Part, as well as in another view it identifies them ; and in 
the other relation, it differences the one Part from the Com- 
plementary Part in one view, as in another it identifies 
them. This is the negative form of thought. 



JUDGMENTS. 39 

Language furnishes modes of Expression for marking these 
diverse movements of thought in the Copula. It represents 
the relation of Whole and Part by such terms as contains, 
comprehends, comprises, and the like ; while it represents the 
relation recognized between Part and Part, by such words 
as implies, involves, and the like. The words, determine, 
condition, and others also express the Copula in its various 
relations. 

In that stricter analysis of thought and expression which 
is necessary in the training of the mind to accurate thinking 
and representation, and which is also required for the criti- 
cal examination of discourse, this diverse mode of determin- 
ing in thought, and of expressing the determination in lan- 
guage, needs to be familiarly known. It will of course be 
understood that such expressions as Virtue is Free, or Vir- 
tue contains Freedom, and Virtue implies Vice, when inter- 
preted in their proper logical significance, mean : Virtue in 
one of its parts is identical with Freedom ; and Virtue is 
identical with Vice in some one respect, that is, as being 
free. 

§ 24. Judgments may be distributed into different sets 
of species, on several distinct principles of divis- Divisi0D of 
ion. As a judgment is made up of internal Judgments. 
form and matter, of thought proper, which is a purely 
subjective element, and the datum to thought, which is a 
purely objective element, the former of which constitutes the 
copula and the latter the terms of the judgment, we should 
anticipate finding in each of these constituents of all thought, 
one or more grounds of distinction. And accordingly, look- 
ing first to the subjective element, the copula, we find that 
there are three different principles of division given in it. 

First, the judgment may vary in respect to its own inter- 
nal and essential nature and irrespectively of its Jf ^ e r ^ e . cfc 
necessary relations to its matter and expression. uia. 

(1.) As to its 

This is the proper quality of a judgment; and in Quality. 



40 PURE LOGIC. 

respect to its Quality, as we have seen, while a Judgment 
may be affirmative or negative, it must be one or the other. 
Strictly speaking, the necessity of judging, when two objects 
of thought are given, either that they are or that they are 
not identical, is imposed upon the Faculty of Thought as a 
pre-determining condition, as the objective Law of Thought; 
while its own proper function lies in taking the one or the 
other of these alternatives — of affirming or denying. We 
may accordingly ground the first division of Judgments on 
their essential Quality. This distinction will give, 1. The 
simple Affirmative and Negative ; 2. The Disjunctive ; — the 
first being grounded on the Subjective Laws of Identity and 
Contradiction ; the second on the Objective Laws of Disjunc- 
tion and Exclusion. The first may be distinguished as of Sim- 
ple Quality ; the last as of Disjunctive Quality. Further, the 
first named species move more freely and characteristically 
in the relation of Whole and Part ; the second in that of 
Part and Complementary Part. 

Secondly, the Judgment may be combined or not with a 
(2.) its Mo- recognition of the ground of its determination. If 
daiity. no t S o combined, the Judgment is pure, simple, or 

unmodified. It is then denominated an Assertory Judgment, 
as it is a mere assertion unmixed with any extraneous ele- 
ment. But the Judgment may take up with itself into the 
same act of consciousness the ground of its determination ; 
it thus becomes so far modified. It is then denominated, in 
distinction from the pure or unmodified — that is, in distinc- 
tion from the Assertory Judgment — a Modal Judgment. 

This principle of distinction in Judgments is what is known 
as the Modality of Judgments. 

The Assertory Judgment, it is obvious, cannot be further 
subdivided in respect to this principle. But the Modal Judg- 
ment can be still further distinguished in respect to the par- 
ticular grounds that may be recognized by the Judgment in 
its determination. These grounds may either lie wholly 
within the sphere of thought, or out of it, that is, in the 



JUDGMENTS. 41 

matter, the datum of thought. If the ground of the Judg- 
ment be recognized as lying wholly within the sphere of 
thought, then there emerges the Necessary or Apodictic 
Judgment. If the ground of the Judgment be recognized, 
and as lying not in the thought, but in the matter of the 
thought, then emerges the Contingent or Problematic Judg- 
ment. 

There may obviously be distinguished subdivisions of the 
Problematic Judgment. The higher grades of these subdi- 
visions, indicated by such modals as probably, possibly, are, 
not unsuitably, recognized in Logical Science. Aristotle in 
his Treatise on Interpretation, enumerates four kinds of prop- 
ositions grounded on their modality: Possible, Contingent, 
Impossible, and Necessary. In his Prior Analytics, he 
speaks only of the Necessary and the Contingent in distinc- 
tion from Pure Propositions. These three primary distinc- 
tions are all that it seems important to notice here. 

The characters of Judgments that are determined by this 
principle of modality, which respects the grounds on which 
the Judgment is recognized, should be carefully distinguished 
from such characters as those of clear, vague, obscure, which 
only look to the degree of consciousness, the mental force or 
energy involved in the Judgment. 

It may further be observed, that the character of neces- 
sary belongs properly, that is, primarily and strictly, only to 
that truth or certainty, the ground of which lies in the 
thought itself exclusively. Thought must ever accept its 
own product as valid and beyond question ; while all beyond 
that, even its own product so far as combined with matter which 
is not of pure thought, it must ever hold as not necessary, 
only problematical. Only the contradictory of pure thought 
can be called absurd in the highest sense. As thought orig- 
inates cognitions, which cognitions may themselves be made 
the object of thought, such cognitions constitute what is called 
Necessary Matter, or as thought, Necessary Truth. All 
other cognitions constitute what is called Contingent Matter 



42 PURE LOGIC. 

or Contingent Truth. As these latter cognitions approach 
more or less nearly to the character of necessary matter, 
they receive in loose unscientific discourse the denominations 
properly belonging to thought alone. We may, indeed, 
classify cognitions in respect to this approximation to Neces- 
sary Truth. In the first and highest class, we should have, 
thus, the pure products of thought, embracing all the rela- 
tions in the Same and Different, the More and the Less, the 
Whole and the Part, the Part and the Complementary Parts, so 
far as these relations are kept pure from matter external to 
thought. Here, accordingly, lie all the truths of Pure Logic 
in the relations of Judgments to one another ; of Concepts, 
also, whether of genus to species, or of attribute to involved 
attribute ; and, moreover, of Reasonings. For a single exem- 
plification in this department of Necessary Truth, that an 
attribute, which is the constituent of another more comprehen- 
sive attribute belonging to a class, belongs to each individual 
of the class, is a Necessary Truth. Here lie, too, all the 
Truths of Pure Mathematics — of Magnitude in Geometrical 
Science, and of Number in Arithmetic and Algebra, and in 
Higher Quantitative Analysis. All these are necessary 
Truths, inasmuch as they are absolute in thought, whether 
there be any extended being to be measured, any real objects 
to be numbered, or not ; whatever may be believed in respect 
to the nature of Space and Time, whether they are realities 
or mere conditions or forms of the Intelligence. Here lie, 
moreover, manifold truths which are applicable to objects 
only so far as they are proper Being — the relations of 
Substance and Quality, of Cause and Effect. These are 
necessary truths for thought, whether external Being be a 
reality or only an idea. 

In the class of Contingent Matter, but more nearly ap- 
proximating the character of Necessary Truth, are the truths 
involved in the relations between the cognitions given in Per- 
ception and Self- Consciousness and those given in Intuition. 
That, for instance, the body which is cognized by perception 



JUDGMENTS. 43 

through the senses exists, is real, and that the mind which 
perceives it also exists, is real, are truths which we loosely 
call necessary truths. They are, obviously, not strictly so, 
for the contradictories of these propositions are not absurdi- 
ties. 

In the same class, but further removed from the class of 
necessary truths, are those expressing relations between any 
two cognitions of Perception. Thus, that the sun is bright, 
is a contingent truth of a lower class in the respect of modal- 
ity than the truth that the sun exists. 

We have, thus, the manifold gradations of modality, rang- 
ing from the faintest possibility up through all the degrees of 
probability and of certainty to the truths of thought, where 
only we find that which is apodictic or absolutely necessary. 

Some logicians, including Sir William Hamilton, have ex- 
cluded from the science this division of Judgments, in respect 
of their modality, as well as the principle upon which it is 
founded, as not of proper logical consideration. Sir William 
Hamilton adduces two arguments for this exclusion. One is 
from Example. He takes the proposition, "Alexander con- 
quered Darius honorably," and asserts that it may be resolved 
into the proposition, "Alexander was the honorable conqueror 
of Darius." By separating thus the word containing the 
copula into its two parts, the copula part was, and the predi- 
cate part conqueror, and thus showing that the modal word, 
honorably, really belonged to the predicate, he fancied he 
showed a universal fact in regard to all forms of expressing 
modality, that they belong properly to the predicate, not to 
the copula — to the matter, consequently, not to the form 
of the thought. But honorably is never a copula modal ; 
and therefore his w r hole argument is fallacious. His other 
argument is, that in order to determine the modality of a 
Judgment, we must go to the matter, for so those logicians 
who have admitted modality as of proper logical considera- 
tion have taught. This argument is valid only against those 
who have taught thus erroneously. 

But the modality regarded by logicians attaches to the 



44 PURE LOGIC. 

copula, not to the predicate ; to the form of the thought, con- 
sequently, not to the matter. And the reasoning by, which it 
is excluded would equally exclude the distinction between 
Affirmative and Negative Judgments ; for it is just as easy 
and just as legitimate to remove the negative from the copula 
to the predicate, as to remove thus the proper copula modal, 
as, indeed, is freely allowed even by those who exclude mo- 
dality, as they expressly but most erroneously teach that the 
proposition A is not B, is exactly equivalent to A is non-B. 
But proper logical modality, as we have seen, like proper 
logical quality, lies in the thought itself, not in the matter. 
We may say, indeed, Alexander possibly conquered Darius, 
or Alexander was a possible conqueror of Darius, and mean 
nearly the same thing. Still, possible conqueror and non-B 
are data presented to thought, while possibly was, like is not, 
is of the essence of the thought itself. One form of expres- 
sion may, under some restrictions, be derived from the other ; 
but to confound them is to confound form with matter, thought 
itself with the mere datum to thought. 

Thirdly, a Judgment may vary according to the degree of 
(3 ) its De- identity recognized between the terms. As this 
gree. identification is total or partial, the distinction gives 

the two species of — 1. Judgments of Total Identity ; and, 2. 
Those of Partial Identity, with their subdivisions. 

This distinction, although at first view it might seem to 
lie rather in the Terms, may yet be not improperly recog- 
nized as a subjective element, lying in the thought itself. 
For, unlike the distinctions that are founded in the matter 
of the thought, this is created in the Thought-process itself 
— in the very act of judging. In the case of the others, the 
objects or terms are presented to the Judgment already dis- 
tinguished, either as objects or as truths, as Comprehensive 
or Extensive Wholes, as Integrate, Substantial, or Causal. 
But here the Judgment itself originates the distinction. The 
two objects are given it simply as wholes. Thought itself 
then recognizes them in relation to their respective parts, 
and identifies some part of one thus recognized with the 



JUDGMENTS. 45 

whole or some part of the other. There is, it is true, a 
seeming impropriety in founding this distinction on the copula. 
But it is only seeming ; for it should be borne in mind that by 
the copula is properly meant the entire product of the judg- 
ing activity in accepting and identifying the data. Whether 
the Judgment shall identify, for instance, a given object with 
more or less of its parts, is determined, not by the datum, but 
by the thought itself. 

Looking next to the objective element in a Judgment, the 
matter or the Terms, we find given in it also a 2 in respect 
threefold distinction. First, the matter as thought, of the Terms. 

— and it is not matter in itself, but only as it is « , Their 
thought, that can be here regarded, — may be either Form - 
itself a Judgment or a simple object of thought. In the latter 
case emerges the proper Categorical ; in the former, the so- 
called Hypothetical, Judgment. 

Secondly, the matter may be thought as in the one or the 
other of the two kinds of Logical Quantity, giving (2.) Their 

i. • * -r* . -, A Logical 

rise to the distinction of intensive and Lompre- Quantity, 
hensive Judgments, according as the terms are thought in Ex- 
tensive or Comprehensive Quantity. 

Thirdly, the matter may be thought in either of the kinds 
of Whole, in which Being is thought, giving rise (3.) Their 

Material 

to the distinction of the three kinds of Judgments Quantity. 

— the Integrate, the Substantial, and the Causal. This prin- 
ciple of distinction may be denominated that of Material or 
Metaphysical Quantity. 

It might at first be supposed that, in making or accepting 
these distinctions, Logic was transcending its sphere as a 
purely Formal Science, and corrupting its own purity by ad- 
mitting what concerns properly the matter of thought. But 
it should be borne in mind that if we think at all we must 
think something — Thought must have an object out of 
itself that is given, presented to it ; and it must think that 
object as it is, not as it is not. It must, therefore, accept the 
matter as it is given. It, however, thinks what is given it 
only in its own proper relations — those of Identity and of 



46 PURE LOGIC. 

Whole and Part. It is of interest to Logic, accordingly, to 
regard the peculiarities of the objects given to Thought only 
so far as they affect the relations of Identity, or of Whole 
and Part. If these peculiarities affect the nature of the 
Whole, Logic must of necessity regard them, or its processes 
of thought become at once invalidated. The purely Formal 
Science of Mathematics presents a perfect analogy in its 
treatment of the wholes or magnitudes in space. It distin- 
guishes a Linear Whole from a Superficial Whole, and both 
from a Solid. Were it to confound these, its procedures 
would be invalid and worthless. So it must accept the dis- 
tinctions between a Right Line and a Curve; between Rec- 
tilinear Surfaces and Curved Surfaces. It must do this be- 
cause the relations of Whole and Part in these several cases 
are different. The sum of the angles in a Rectilinear Tri- 
angle does not correspond with the sum of the angles in a 
Spherical Triangle. Any Formal Science must, therefore, 
be able to distinguish such peculiarities in its matter as affect 
the purity and validity of its formal processes. In other 
words, Logic, although, or perhaps more accurately, because, 
a Formal Science, must evolve its principles in such a way 
as to meet the peculiarities of the matter to which it is to 
apply its formal procedures. 

At the same time, Logic does not scrutinize the reality of 
the matter given it to be thought, except, at least, to see that 
it does or does not correspond with its own principles, as 
whatever contradicts those it is bound to reject. It does not 
affect its Laws or the integrity and validity of its processes 
whether there be, in point of fact, any such distinctions in 
the matter as are given to it ; as Mathematics does not in- 
quire whether there be in nature Lines, Surfaces, Solids, its 
procedures being just as legitimate and sure, if there were 
nothing in reality in the outer world to correspond to these 
distinctions. It is sufficient to vindicate the propriety and 
the necessity of regarding these cogitable distinctions in mat- 
ter, simply to consider that these distinctions are, in fact, 
cogitable — that they are possible to thought. 



JUDGMENTS 



47 



The limits to be placed in regard to the extent to which 
these distinctions should be admitted are to be determined by 
the proposed objects and uses of the Science. A system of 
general Logic should admit only the most general distinc- 
tions. It should not certainly stop short of those which are 
found in the two forms in which Being is known to us — 
Substance and Cause. 



Judgments 
are divided, 



These six Divisions of Judgments, it should be observed, 
are, in reference to one another, Cross Divisions or Con- 
divisions, and intersect one another. The same Proposition, 
thus, may be Affirmative, Assertory, Partial, Categorical, 
Comprehensive, and Substantial. 

With these general views, in regard to the grounds of the 
distinctions to be recognized in Logical Judgments, we pro- 
ceed to a particular consideration of them in order, present- 
ing first the following tabular view : — 

f 1. As to its Quality, into (1.) 
Simple Affirmative and 
Negative ; (2.) Disjunc- 
tive. 

2. As to its Modality, into 
(1.) Assertory ; (2.) Prob- 
lematic ; (3.) Apodictic. 

3. As to its Degree, into (1.) 
Identical; (2.) Partial. 

1. As to their Form, into 
(1.) Categorical ; (2.) Hy- 
pothetical. 

2. As to their Logical Quan- 
II. The Terms, i tity, into (1.) Comprehen- 
sive ; (2.) Extensive. 

3. As to their Material Quan- 
tity, into (1.) Integrate ; 
(2.) Substantial ; (3.) Cau- 
sal. 



In respect of ^ 
I. The Copula, 



48 PURE LOGIC. 

§ 25. The First General Division of Judgments is 
1 First Di- f° uncIie d on tne Quality of the Copula, and gives 
virion of as its results the two kinds of — 1. Simple Affirm- 

Judgments , . . . ' . M 

—as to ative and Negative ; and, 2. Disjunctive Judg- 
ments. 
An Affirmative Judgment is a product of positive 

(1 ) Affirma- thought recognizing sameness between the Terms ; 
tiye - as A is B ; Virtue is Manliness ; The Skies are 
Blue. 

The copula in the simple Affirmative Proposition is ex- 
pressed in Mathematical Science by the symbol of Equality 
or Identity (=) as a=b. .In common discourse, the inflec- 
tions of the verb to be are used to express the simple copula. 

A Negative Judgment is a product of negative thought 

(2 ) Nega- recognizing difference between the Terms ; as A 
tive - is not B ; Virtue is not Necessity ; The Shies are 
not Cloudy. 

A Disjunctive Judgment is a necessitated product of 
(3.) Disjunc- thought, identifying an object with another, or 
tive. w jth its different, as A either is or is not B ; vir- 

tue is either voluntary or involuntary ; the shies are either 
light or dark ; the flower is either blue or purple. 

The copula is expressed with the aid of the disjunctive 
particles, as is either — or. The first of this pair of particles 
is often omitted, and then the expression is equivocal, for the 
or may indicate an alternative in the words only and none in 
the thought, as in the proposition, the electricity was vitreous 
or positive. 

There are three distinct forms of this species of Judgment, 
Logical op- founded on the diverse kind of difference, or, as 
position. logicians designate it, of Opposition, that may be 
thought in the Judgment. First, the primitive form is where 
the opposition or difference lies in the copula itself; as A is 
B or is not B ; virtue either is voluntary or is not voluntary. 
This must be regarded as a single judgment, not a compound, 
for it is a single act of thought, although embracing more 



JUDGMENTS. 49 

than one element or factor. In this case we have what is 
called Pure Contradictory Opposition, The Law of Exclu- 
sion forbids any negative Judgment of this form. 

But an immediate derivative from this is effected by the 
transfer of the negation or sign of difference to the predi- 
cate — a transfer which although not always, yet is often 
legitimate in thought, as will be shown hereafter. So that 
from this primitive Judgment we obtain the form, A is B or 
not B ; Virtue is voluntary or involuntary. In this form, 
while the opposition is no longer in the copula, but in the 
predicate, the opposition is between only two parts or mem- 
bers of the predicate, and is of such a nature that one by the 
necessities of thought excludes the other. This is called 
Contradictory Opposition ; but, evidently, it is not necessa- 
rily pure, or of the thought merely ; it is only accepted or 
assumed as contradictory. To assure perfect thought, it will 
be necessary often to reduce the Judgment to pure contra- 
dictory opposition. The fallacy arising from accepting oppo- 
sition in the terms for opposition in the copula, is a very 
common one. 

From this second form of a Disjunctive Judgment, there 
springs a third, in which the opposition between the parts 
of the predicate is not of such directly contradictory character, 
as that the one of necessity excludes the other, as in the prop- 
osition : The flower is either blue or purple. If the flower be 
not blue, it does not necessarily follow that it is purple ; it 
may be of some other color, although it cannot be, at the same 
time at least and in the same part, both blue and purple. 
This kind of opposition in the terms of a Judgment is called 
Contrary Opposition, We have thus the following distinc- 
tions : — 

§26. Disjunction in Thought maybe either in Its kinds: 
the Copula or in the Terms. If it be in the Cop- dicfrory^2~ 
ula, we have Pure Contradictory Opposition, Contrary. 

If it be in the Terms, it is either of Contradictory or of 
Contrary Opposition. 
4 



50 PURE LOGIC. 

The Opposition is Contradictory when it lies be- 
tween two objects of thought, one of which necessarily, that 
is, in strict thought, excludes the other. 

It is Contrary when it lies between two or more objects, 
so that the denial of one does not directly and necessarily 
imply the admission of the other, or the reverse. 

It will have been observed that these several forms of Dis- 
junction really work so many gradations in the logical rigor 
of the Thought. Only the first, which indeed the Definition 
properly respects, is a disjunction of strict logical necessity. 
The form A is B or is not B, holds necessarily true univer- 
sally, as no two objects can be brought before the mind in re- 
gard to which Thought is not necessitated to affirm that they 
are either the same or are not the same. But the second 
form or gradation does not hold universally ; for we cannot 
say Sweetness is voluntary or involuntary, since it is neither. 
Only when this form can be reduced to the first is it of 
necessary cogency. The third form or gradation is still 
further removed from the character of a necessary logical 
form. To insure for it this character, it must be reduced 
through the second to the first. 

It is remarkable that logicians, who have been most rigid 
in insisting that Logic must be held to the pure form of 
Thought to the utter exclusion of all consideration of the 
matter of Thought, have admitted the second of these forms 
of Disjunction without a question, and have overlooked en- 
tirely the first, which is the only one that lies in the pure 
form of the Thought. 

The examples given express a disjunction only in the pred- 
icate of the Judgment. But it may lie equally well in the 
subject ; thus, either A or B is G, is just as legitimate a 
Judgment as G is A or B. So the negative form is equally 
competent. Examples in concrete matter are : either John or 
James is guilty ; neither James nor John is guilty. This neg- 
ative form corresponds with what has- been called the Re- 
motive Judgment, which is classed as a species of Composite 



JUDGMENTS. 51 

Categorical Judgments. 1 A Judgment, also, Disjunctive in 
form, may be sometimes equivalent to what has been termed 
the Divisive Judgment, which has been classed as a species 
of Categorical Judgments ; * as, Triangles are either Equilat- 
eral^ Isosceles, or Scalene, which is equivalent to Triangles are 
partly Equilateral, partly Isosceles, partly Scalene, 

§ 27. The Second General Division of Judgments is 
founded on the Modality of the copula or deter- Second Di- 

• • , . ,, T , . rr,, . ,. .4 . vision of 

mining act in the Judgment, lhis distinction Judgments 

, t , 7 n as to their 

gives the three species of — Modality. 

1. The Assertory. 

2. The Problematic. 

S. The Apodictic, or Necessary. 

An Assertory Judgment simply affirms or (1 . Assert . 
denies : as, A is B ; A is not B ; A is either B or C. ov y- 

A Problematic Judgment affirms or denies under the 
modification of Contingency: as A may be B ; A (2.) prob- 
may be either B or 0. lematic - 

An Apodictic or Necessary Judgment affirms or 
denies under the modification of Necessity : as, A (s.) Apodio- 
must be B ; A must be either B or G; A is neces- tlc ' 
sarily B. 

The Modality of a Judgment may be expressed by modals, 
or, as they are sometimes called, modal adverbs, as well as by 
the mood inflections of the verb to be. Thus probably, pos- 
sibly, contingently, perhaps, by chance, it may be, and the like 
adverbial expressions, are Copula Modals appropriate to the 
Problematic Judgment. The characteristic of this Judgment 
is that in it the ground of the identification of the terms is 
accepted or assumed as in the matter, and not contained in 
the Thought itself. As in the second and third forms of 
the Disjunctive Judgment, so here, the problematic in the 
matter may be taken or assumed as partaking of the char- 
acter of necessity, which properly comes from the Thought 
alone. This assumption is not, however, of strict right, but, 
so to speak, only by courtesy. 

1 Drobisch, LogiJc. §§ 44, 45. Leipzig, 1851. 



52 PURE LOGIC. 

The modals which are appropriate to Apodictic Judg- 
ments are such as necessarily, unavoidably, of or by necessity. 
mu- *^- ■ § 28. The Third General Division of Judg- 

ionofjudg- merits is founded on the Degree of Identity predi- 

ments, as to 

their Degree cated. This Identity may be Total or Partial, 

of Identity. . . . * * 

giving rise to the two species or — 

1. Judgments of Total Identity. 

2. Judgments of Partial Identity. 

These varieties of Judgments have been termed Substitu- 
tive and Attributive — a denomination not pointing to the 
essential ground of the distinction. It is true that in those 
of the first species in which a total identity is affirmed be- 
tween the subject and the predicate, the terms are converti- 
ble — may be substituted one for the other. But precisely 
so in every Judgment, so much of either term as is taken is 
exactly convertible with whatever part of the other is taken 
in the Judgment ; and so far as the validity of the Judgment 
is concerned, it is a matter of entire indifference which is 
made the subject or which the predicate. It is the occasion 
of the use which ever determines this. And in regard to 
the name given to the other species, Attributive, all Judg- 
ments are attributive, since it is of their very essence that 
they attribute. 

The first of these two species of Judgments regarded as 
expressed, that is, as Propositions, embraces two varieties. 
1. The Tautological, in which, the terms are expressed in the 
same verbal form, as, A is A. 2. Proper Identical, in which 
the Terms are expressed in different forms of words, as, Virtue 
is manliness ; likewise in Algebraic Formulas, as, a = b -j- c ; 
and in Exact Definitions, as, Virtue is right action. 

Those of the other species make up the great body of prop- 
ositions occurring in discourse. In them one of the terms 
is always affirmed to be related to the other as Part to a 
Whole. Thus in the Proposition Man is two-footed, the char- 
acter two-footed is affirmed to be one of the characters that 
make up the whole notion, man. In the Proposition Man is 



JUDGMENTS. 53 

a biped, man is affirmed to be a part of the class of objects 
called bipeds ; or, what is an exactly equivalent explication 
in the former proposition, one of the parts of the whole 
notion, man, is identified with the character two-footed ; in 
the latter, the part or species, man, is identified with one of 
the parts that make up the whole genus, biped. 

It will be convenient, and will involve no serious liability 
to error, if we adopt the familiar designations of Identical 
Judgments and Partial Judgments for the two species of this 
class. We then have the following definitions. 

An Identical Judgment is one in which the subject is 
identified wholly with the predicate; as, a = b; n > Identi _ 
Virtue is manliness ; Man is rational animal. caI - 

A Partial Judgment is one in which the subject is but 
partially identified with the Predicate, in which 

, r • .-,, i m . ( 2 -) Partial. 

case the relation recognized between the lerms is 

that of Whole and Part; as, Man is rational; Man is a 

biped. 

A Tautological Proposition is one in which the 
Terms are expressed in the same verbal form ; as , 3 , Taut0 . 
a is a ; Gold is gold. lo s icaL 

§ 29. The Fourth General Division of Judgments is 
founded on the diverse character of the Terms. Fourth Di- 
These we have found to be of three classes. 1. Judgments 
Individual or Simple Objects. 2. Concepts. And, character of 
3. Judgments. Those Judgments which have for their Terms. 
their Terms other Judgments, possess some peculiar charac- 
ters which make it desirable to keep them distinct from the 
others. They have been in fact familiarly distinguished by 
the denomination of Hypothetical, while other Judgments 
have been called simply Categorical. We have thus the fol- 
lowing definitions. 

A Categorical Judgment is one the Terms of which 
are Individual or Simple Objects or Concepts; as, (1 * categor- 
Bucephalus is a quadruped; Man is rational ; icaL 
Fire burns. 



54 PURE LOGIC. 

A Hypothetical Judgment is one the Terms of which 
(2.) Hypo- are Judgments; as, If A is B, C is D ; If virtue 
theticai. j s voluntary, vice is voluntary ; That A is B im- 
plies that G is D. 

This last species of Judgments has received its name from 
the verbal form in which they more commonly appear. They 
are ordinarily expressed under the form of an hypothesis or 
condition indicated by the conjunction if It must not be 
supposed that this suppositive or conditional character reaches 
beyond the Terms of the Judgment, or affects at all the ab- 
solute nature of the Judgment itself. The relation of iden- 
tity between the Terms is just as absolute as in any Judg- 
ment. But the assumed character of the datum, or matter, 
is here, through the imperfections of language, signalized by 
the conjunction prefixed to the term ; as where a judgment 
is used as an object of thought, we ordinarily mark it as thus 
used by a grammatical conjunction, such as if and that. 

It is to be noticed here that, as elsewhere more fully ex- 
hibited, there are two fundamental relationships in Thought 
as essentially regulated by Quantity ; the one between the 
Whole and Part, the other between a Part and its Comple- 
mentary Part. The first is the only relationship in which 
logicians have exhibited Thought; and all their teachings 
and their illustrations have been confined to that. Perhaps, 
for the sake of simplicity, it may be expedient to limit the 
illustrations, generally and introductory, to a single and a 
more familiar relationship. But it would involve serious 
error if that should be throughout exhibited as the only rela- 
tionship in Thought. And here, precisely, in their treatment 
of Hypothetical Judgments, logicians have experienced the 
evil consequences of partial and one-sided views, as their ex- 
positions of this product of Thought are discordant and con- 
fused. It should be distinctly noticed then, that under the 
common form of the Hypothetical Judgment, either of the 
two relationships of Quantity, of Whole to Part, or of Part 
to Complementary Part, may be indicated. Thus in the 



JUDGMENTS. 55 

Judgment, If virtue is free, temperance is free, the relation- 
ship is that of Whole to Part ; while in the Judgment, If 
virtue is free, vice is free, it is that of Part and Complement- 
ary Part, virtue and vice being complementary parts of the 
whole — free action. 

In either case the antecedent clause is said, indifferently, to 
determine, to condition, to imply, or to involve the consequent 
clause, or the reverse. For it is to be remarked, that the 
consequent or predicate clause may condition as well as be 
conditioned by the other. This is, however, not to be taken 
unqualifiedly and without explanation. For while in the case 
in which the movement of Thought is between Complement- 
ary Parts, the two clauses may, of course, — except as one is 
assumed as a positive, and the other as a negative, — stand in 
perfectly reciprocal relations ; in the other case, the whole 
conditions the part otherwise than as the Part the Whole. 
Thus vice, as complementary part, conditions virtue as much 
and in the same way as virtue conditions vice ; but temper- 
ance conditions virtue as containing it as one of its constitu- 
ent characters, while virtue conditions temperance as being 
contained in it. 

A hypothetical Judgment has both its Terms Judgments. 
If but one Term be a Judgment, as may be the case, the 
. Judgment is classed as Categorical. 

§ 30. The characteristics of the Hypothetical and the 
Disjunctive Judgment may both concur in the same Hypothetico . 
Judgment; we then have the Hypothetico-Disjunct- Disjunctive. 
ive, or, as it has been called, the Dilemma ; as, If A is B it 
is either G or non- C ; If an action be prohibited, it is pro- 
hibited by natural or by positive law. The explication of 
this Judgment is easy. The former of these examples 
means : The truth that A is i? contains or involves the truth 
that A is either or non- G The latter means : The truth 
that an action is prohibited involves the truth that it is pro- 
hibited by natural or by positive laws. We thus have the 
definition : — 



56 PURE LOGIC. 

A Hypothetico-Disjunctive Judgment is a Disjunct- 
ive Judgment with truths or judgments instead of simple 
objects for its Terms. 

It may be remarked here that Judgments of different 
classes may be combined almost indefinitely ; but this par- 
ticular combination of the Disjunctive with the Hypothetical 
has attained a classical distinction from its use by old Gre- 
cian sophists. 

§ 31. The Fifth General Division of Judgments is 
Fifth Divis- founded on the two kinds of Logical Quantity — 
ionofjudg- Extensive and Comprehensive or Intensive — 

ments, as to r m 

their Logical which give the two species of Extensive and Corn- 
Quantity. . f 

prehensive or Intensive Judgments. 

An Extensive Judgment is one in which the Terms are 
(l.) Exten- ta ken in the Quantity of Extension ; as, Bucepha- 
eiTe * lus is a quadruped ; that is, Bucephalus is one of 

the class quadruped. 

A Comprehensive or Intensive Judgment is one in 
(2.) Compre- which the Terms are taken in the Quantity of 

hensive or _, . _, _ . _^ 

intensive. Comprehension ; as, Bucephalus is four-footed ; 
that is, Bucephalus in one of his attributes is four-footed, or 
Bucephalus contains the character four-footed. 

In an Extensive Judgment, when affirming only partial 
identity, the predicate is affirmed to stand in the relation of 
whole to the subject. In a Comprehensive Judgment, .when 
of partial identity, the subject is the containing whole, and 
the predicate is the part affirmed in the Judgment to be con- 
tained in the subject. 

Before Sir William Hamilton, logicians had generally 
viewed all propositions as being of Extensive Quantity only. 
They accordingly divided them into four species, viz : 1. 
Universal, in which the subject is taken in its entire sphere, 
as, All men are mortal. 2. Particular, as Some men are 
learned. 3. Individual or Singular, in which the subject is 
an individual. And, 4. Indefinite, in which the subject is 
not articulately declared to be either Universal, Particular, 



JUDGMENTS. 57 

or Singular. Rejecting this division, Hamilton proposes that 
the subordinate divisions of Judgments in respect of their 
Extensive Quantity be those of — (1) a Determinate, and (2) 
those of an Indeterminate, Quantity ; the former including 
the Universal as one species, and the Individual as the other 
species, and the latter class corresponding to the Particular. 

The two kinds of Judgments determined in respect of their 
Quantity, as Universal and Particular, being combined with 
two determined by their simple Quality, the Affirmative and 
the Negative, in their diverse combinations give rise to four 
species : the Universal Affirmative, the Universal Negative, 
the Particular Affirmative, and the Particular Negative ; 
and, to facilitate the statement and analysis of the syllogism, 
these four have by logicians been designated by the vowels 
A, E, I, O. The Universal Affirmative are designated by 
A ; the Universal Negative by E ; the Particular Affirma- 
ative by I ; and the Particular Negative by O. 

But this classification originating in an extremely limited 
view of the diverse character of Judgments, and overlooking 
the distinctions both of Logical and of Material or Meta- 
physical Quantity, as well as excluding all consideration of 
Disjunctive and Hypothetical Judgments, may well be dis- 
carded. It deserves mention only as of the past and as his- 
torical. 

§ 32. The Sixth General Division of Judgments is 
founded on the Material or Metaphysical Quantity sixth Dms- 
of the Terms, as forming Integrate, Substantial, or men°t s as fo 
Causal Wholes. This distinction gives rise to the whoSin the 
three species of Integrate, Substantial, and Causal Terms - 
Judgments. 

An Integrate Judgment is one in which the Terms are 
regarded as Integrate Wholes ; as, a=5-|-c; Man (*•) J- nte " 
is Soul and Body. 

A Substantial Judgment is one in which the Terms 
are viewed in the relations of a Substantial Whole, (2 , Sut)S tan- 
that is, of Substance and Attribute; as, Man is tiaL 
rational. 



58 PURE LOGIC. 

A Causal Judgment is one in which the Terms are 
(3.) Causal. v i ewe d * n tne relations of a Causal Whole, or of 
Cause and Effect ; as, John is studying ; The Sun 
illuminates the planets. 

The Copula in the Integrate Judgment is variously ex- 
pressed in language, as by is, consists of, is composed of, is 
constituted of, is made up of equals, is equivalent to, is iden- 
tical with, is the same as, and the like. 

In the Substantial Judgment it is expressed by is, contains, 
comprehends, includes, involves, implies, and the like. 

In the Causal Judgment it is generally and distinctively 
expressed by inflections of verbs, as illuminates, produces, or 
by is, with participial forms, as, is illuminating, is producing. 

The expressions vary according as the Whole or the Part is 
presented as the Subject in the Judgment. Thus when the 
Whole is the Subject, the forms in the Integrate species are : 
Man is composed of soul and body; Virtue comprehends 
freedom ; Heat expands bodies. When the Part is the Sub- 
ject, the forms are such as these : Soul and Body compose 
man ; Freedom is comprehended in virtue ; Bodies are ex- 
panded by heat. 

The relations between the Whole and the Parts are indi- 
cated by prepositions: in the Integrate Whole by of, as, 
Body and Soul are parts of man ; in the Substantial and in 
Comprehensive Quantity, by in, as, Rational is contained in 
man ; in Extensive Quantity, by under, as, African is con- 
tained under man ; in the Causal, by through or by, as, Bod- 
ies are expanded by heat. 

§ 33. In their relation to one another, Judgments are 
*f S j n d * ionS distinguished in various ways. It will be sufficient 
merits in re- to state in a summary manner such distinctions as 

lation to one , , ._ _ 

another. nave been more generally recognized. 

The most important of these relations is that which arises 
from the transposition of the Terms, so that the 

Conversion. . 

Subject and the Predicate change places. This 
transposition is technically called Conversion, and the prop- 



JUDGMENTS. 59 

osition arising from the conversion is called, in relation to 
the proposition in its first form, the Converse. Thus, Eight 
free action is virtue is the Converse of Virtue is right free 
action. 

" When the matter and form of two Judgments are con- 
sidered as the same, they are called Identical, Con- j udgmeilts 
vertible, Equal, or Equivalent (propositiones iden- identical. 
ticce, pares, convertibiles, ccquipollentes) ; on the 
opposite alternative, they are called Different (pr. 
diver see). If considered in certain respects the Relatiyely 
same, in others different, they are called Relative- identical. 
ly Identical, Similar, or Cognate {pr. relative identicce, simi- 
les, affines, cognatce). This resemblance may be either in 
the subject and comprehension, or in the predicate and ex- 
tension. If they have a similar subject, their 
predicates are Disparate (disparatd) ; if a similar ispara e * 
predicate, their subjects are Disjunct (disjuncta). Disjunct. 

" When two judgments differ merely in their quantity of 
extension, and the one is, therefore, a particular, the other 
a general, they are said to be subordinated, and their rela- 
tion is called Subordination (subordinatio). The gult)alter . 
subordinating (or as it might, perhaps, be more nant - 
properly styled, the super ordinate) judgment, is called the 
Subalternant (subalternans) ; the subordinate judg- gubalter . 
ment is called the Subalternate (subalternaturn). nate - 

" When, of two or more judgments, the one affirms, the 
other denies, and when they are thus reciprocally opposition of 
different in quality, they are said to be Opposed Judgments. 
or Confiictive (pr. oppositce, dj/ri/cci/xei/ai), and their relation, 
in this respect, is called Opposition (oppositio). This oppo- 
sition is either that of Contradiction or Repugnance (contra- 
dictio, dvrtc^acrts), or that of Contrariety (contrarietas, Ivav- 
tlottjs). 

" If neither contradiction nor contrariety exists, the judg- 
ments are called Congruent (pr. congrue??tes, con- Congruent 
sonantes, consentientes). In regard to this last state- Judgments. 



60 PURE LOGIC. 

Subcont ment it is stated in logical books, in general, that 
opposition, there is an opposition of what are called Subcon- 
traries (subcontraria), meaning by these particular proposi- 
tions of different quality, as, for example, some A are B, 
some A are not B ; or, some men are learned, some men are 
not learned ; and they are called Subcontraries, as they stand 
subordinated to the universal contrary propositions — All A 
are B, no A is B ; or, All men are learned, no man is learned. 
But this is a mistake ; there is no opposition between Sub- 
contraries ; for both may at once be maintained, as both at 
once must be true if the some be a negation of all. They 
cannot, however, both be false. The opposition in this case 
is only apparent ; and it was probably only laid down from 
a love of symmetry, in order to make out the opposition of 
all the corners in the square of Opposition, which may be 
found in many works on Logic. 

"It may be proper to add certain distinctions of judgments 
Distinction an( ^ propositions, which, though not strictly of a 
of Proposi- logical character, it is of importance should be 

tions not '° . . 

strictly logi- known. Considered in a material point of view, 

all judgments are, in the first place, distinguished 

Theoretical m ^ Theoretical and Practical. Theoretical are 

and rracti- 

caL such as declare that a certain character belongs or 

does not belong to a certain object ; Practical, such as declare 
that something can be or ought to be done-— brought to bear. 

" Theoretical, as well as practical judgments, are either 
indemon- Indemonstrable, when they are evident of them- 
Demons^ra- selves ; when they do not require, and when they 
ble * are incapable of proof: or they are Demonstrable, 

when they are not immediately apparent as true or false, but 
require some external reason to establish their truth or false- 
hood. 

" Indemonstrable propositions are absolute principles (apxat, 
principid) ; that is, from which in the construction of a sys- 
tem of science, cognitions altogether certain not only are, but 
must be, derived. Demonstrable propositions, on the other 



JUDGMENTS. 61 

hand, can, at best, constitute only relative principles ; that is, 
such as, themselves requiring a higher principle for their 
warrant, may yet afford the basis of sundry other proposi- 
tions. 

"If the indemonstrable propositions be of a theoretical 
character, they are called Axioms ; if of a practi- Axioms and 
cal character, Postulates. The former are princi- Postulates. 
pies of immediate certainty ; the latter, principles of imme- 
diate application. 

" Demonstrable propositions,* if of a theoretical nature, are 
called Theorems (theoremata) ; if of a practical, 
Problems (problemata.) The former, as proposi- andProb- 
tions of a mediate certainty, require proof ; they, 
therefore, consist of a Thesis and its Demonstration ; the 
latter, as of mediate application, suppose a Question (quces- 
tio) and its Solution (resolutio). 

"As species of the foregoing, there are, likewise, distin- 
guished Corollaries (consectaria, corollaria), that 
is, propositions which flow, without a new proof, 
out of theorems or postulates previously demonstrated. Prop- 
ositions, whose validity rests on observation or experiment, 
are called Experiential^ Experimental Proposi- Experiment- 
tions (empiremata, experientice, experimentd) ; ^ Pr °p°si- 
Hypoiheses, that is, propositions which are as- 
sumed with probability, in order to explain or 
prove something else which cannot otherwise be explained or 
proved ; Lemmata, that is, propositions borrowed 
from another science, or from another part of the 
science, in order to serve as subsidiary propositions 
in the science of which we treat ; finally, Scho- 
lia, that is, propositions which only serve as illustrations of 
what is considered in chief. The clearest and most appro- 
priate examples of these various kinds of propositions are 
given in mathematics." 



CHAPTER V. 

THE PRODUCTS OF THOUGHT. II. CONCEPTS. 

§ 34. The Second gradation of Thought is the Concept. 
It is derived from the primitive product, the Judgment, by 
Formationof an act °^ svntn esis or composition. It accordingly 
Concepts. presupposes two or more Judgments, and, if a valid 
product of Thought, can always be resolved back into them. 
It can, in fact, be verified only by being thus referred back to 
the Judgments from which it is derived. It is formed either 
by the synthesis of the Subjects of two or more Judgments, 
or by a synthesis of their Predicates — an alternative which 
gives rise to the two fundamental classes of Concepts. It 
may conduce to clearness to exemplify the process of forming 
the Concept in these two ways separately. 

First, then, if we synthesize the subjects, the procedure 
will be as follows : The Judgments, out of which the Con- 
cept is to be formed, we will assume to be — Socrates is ra- 
tional ; Cicero is rational ; James is rational. By uniting 
the subjects, we have Socrates and Cicero and James, and 
marking the union by a single term which shall embrace them 
all in one, we will say, man, we have the union signalized in 
language. This union of the differing subjects of several 
propositions having a common predicate is called a Concept ; 
in this case a Concept in Extensive Quantity. The formula 
for the formation of all Concepts of this class is, accordingly : 
The Judgments, B is A, C is A, give the Concept (B-\-C) 9 
or when signalized in language by one term, the Concept D; 
or in brief: The Judgments B is A, C is A, give 5-J-C= 
the Concept D. 



CONCEPTS. 63 

The procedure in forming Concepts of the other class is 
analogous. Here the Subject remains the same, and the 
Concept arises from the synthesis of the Predicates which 
differ. Thus, the Predicates in the Judgments, Socrates is 
rational, Socrates is animal, being united, we have rational 
and animal, or signalizing the union by a single term, we 
have the Concept, Man. The term Man here, it will be ob- 
served, means a complement of attributes, as rational, ani- 
mal, not, as before, of subjects, as Socrates, &c. This is a 
Concept in Comprehensive Quantity ; the formula of which 
is : The Judgments A is B, A is C, give, by synthesis of the 
differing Predicates, the aggregate (£-\-G), which signalized 
as one in Language is expressed by D. Or the Judgments 
A is B, A is C, give Concept (B-\-C) = Z>. 

§ 35. A Concept may be defined, accordingly, to be a 
product of Thought, resulting from the synthesis p efin itionof 
of the Subjects or of the Predicates in several Concept. 
Judgments. 

The common Subject in a Predicate- Concept, or the com- 
mon Predicate in a Subject- Concept, on which the Concept 
is formed, is called its Base. 

The name, Concept, is derived from the Latin word Con- 
ceptum, meaning something taken with another. The corre- 
sponding word used to denote the act of forming a Concept is 
Conception, which is also in common discourse often used to 
denote the product. It is used, in fact, like other words of 
this kind, in the threefold import of faculty, act, and product. 

§36. The Law of Identity, or as, in its fuller expression, 
it may be denominated, the Law of the Same and 

. . Concepts un- 

Different, it will have been seen, presides over this der Law oi 
product of Thought, as over the Judgment. No 
valid Concept can be formed, unless from Judgments which 
have either identical subjects or identical predicates. The 
Concept arises from the Synthesis of the different under the 
same ; of different subjects having the same predicate, or of 
different predicates having the same subject. In other words, 



64 PURE LOGIC. 

in the Base is to be found the identifying principle governing 
in the Concept. 

§ 37. It will have been observed, moreover, from the 
Concept a mode of its formation, as given in § 34, that a 

RelativeCog- _. . . ' - . , , . ..-''• 

nition. Concept is essentially a relative cognition. It is 

not only the result of a synthesis, not only the aggregate of 
a plurality of Judgments, and accordingly of relative cogni- 
tions, but the cognitions that are brought together in this 
synthesis sustain a determined and peculiar relation to one 
another. If the Concepts be formed from the subjects of the 
Judgments, those Judgments must have a common — the 
same predicate ; if from the predicates, the Judgments must 
have the same subject. Concepts are thus from their very 
nature relative cognitions, and the principle of relation is in 
the sameness of the term of the Judgment which is not syn- 
thesized into the Concept — in its Base. 

Concepts, however, differ from Judgments, as relative cog- 
nitions, in this respect : that in the Judgment the relation is 
explicit, while in the Concept it is only implied. Thus in 
the Judgment, Man is rational animal, the relation is ar- 
ticulately declared ; but in the Concept, Man, the relation to 
the other term of the Judgment from which it is derived, 
although real, is not expressed, but only implied. The Base 
of the Concept, although real, is not expressed. 

§ 38, Still further, a Concept is essentially a one-sided 
Concept a cognition. It is formed from but one side of a 
Cognition. Judgment, from the Subject or from the Predi- 
cate. It may be regarded, indeed, as an aggregate of Judg- 
ments, that is, a synthesized or composite Judgment, with the 
single term — the Base, and the Copula dropped. 

A Concept, however, always implies the Judgments from 
which it is derived; it implies the other term, which has 
been dropped, but which is the indispensable condition of its 
being formed, and is, therefore, appropriately denominated 
the Base of the Concept ; and also implies that this Base 
has been identified with each of the terms which compose 
the Concept. 



CONCEPTS. 65 

Although a Concept has this character of one-sidedness, it 
must not be supposed that it is properly an inadequate cog- 
nition, as some logicians have taught. * Of all objects of 
thought, that of a Concept is most exactly and adequately 
embraced in the thought ; of all object-cognitions, the cog- 
nition in a Concept is the most adequate. A Concept is not, 
indeed, an adequate cognition of any individual embraced 
under it, or of any simple attribute embraced in it. But 
these are not the objects thought in Concepts. A Concept 
is ever just the cognition of the subjects embraced under it 
or the predicates embraced in it ; it is of course a perfectly 
adequate cognition of its proper object. 

From the inadequacy of language to express perfectly and 
fully the characters of thought, a word expressing a Concept 
is for the most part at least used indifferently both for a sub- 
ject-concept and also for a predicate-concept. Man, thus, both 
denotes an aggregate of subjects, as Socrates, &c, and also of 
predicates or attributes, as rational, &c. For accurate and 
valid Thought, it becomes necessary to distinguish these uses ; 
or, out of the confusion, error will be likely to arise. This 
distinction is sometimes marked, when a Concept is used as a 
term of a Judgment, by some peculiarity in the form of ex- 
pression. Thus in the propositions, Man is two-footed, Man 
is a bi-ped, in the former, the Concept, Man, is obviously a 
predicate-concept ; in the latter, a subject-concept. Often 
the distinction emerges only in the more advanced progress 
of the thought, as in a course of reasoning. It is natural to 
anticipate that the confusion might, in continued discourse, 
bring in serious error which, could not be corrected nor indeed 
be brought to light without the application of the distinction. 
This will, in the proper place, be fully exemplified. It is 
sufficient here to expose the reality and the probable impor- 
tance of the distinction to correct and valid thought. 

§ 39. It will occur to the reflecting mind, on this exposition 
of the mode in which Concepts are formed, that Conceptsnot 
they are mere products of Thought, aggregates of Katies, 
5 



66 PUKE LOGIC. 

Subjects, or aggregates of Predicates, and do not imply ne- 
cessarily any exactly corresponding aggregates in the reality 
of things. How many individual subjects of Judgments shall 
be combined, or how many predicates, are questions that will 
be determined by such considerations as those of extent of 
observation, practicability of aggregation, convenience of use, 
the needs of occasion, and the like. The extent of the aggre- 
gation, therefore, varies indefinitely with the occasions of 
Thought ; and it is not to be supposed that the constitution 
of things around us fluctuates precisely with the fluctuations 
of Thought. As the mathematical analyst, in the progress of 
his demonstration, finds it convenient to substitute single 
letters or symbols to denote a number of quantities in some 
respect of like character, so Thought, for its own manifold 
conveniences, often aggregates like elements and signalizes 
them by single words. It does not thereby change the con- 
stituted system of> things. 

Concepts, thus, and so the words in which they are embod- 
ied and maintain their existence, are not fixed and constant 
as inhering in the stability and constancy of nature. They 
rise and sink with the ever- varying vicissitudes of occasion. 
They are not, however, any more than the assumed general 
symbols in a mathematical process, illusory and empty. They 
are ever significant ; they ever suppose and express what is 
similar, or rather, express recognized identities in the objects 
of thought. They can, in fact, simply by reversing the proc- 
ess by which they were formed, ever be traced through the 
Judgments back to the realities from which they originally 
sprang, or, at least, to the primitive cognitions brought to 
Thought by the proper Present ative Faculties. 

In our endeavors to realize a concept, that is, to ascertain 
How to real- what exactly of reality it expresses, what in the 

ize a Con- . - A * y 

cept. reality of things around exactly corresponds to it, 

how far and in what respects it is a true, trustworthy cogni- 
tion of the realities to which it applies, we must not expect 
of course to find an object that is exactly commensurate with 



CONCEPTS. 67 

the Concept ; that is, an aggregation of just so many sub- 
jects, no more, no less, having the single predicate under 
which we have found the Concept, or an aggregation of just 
so many attributes belonging to the single subject under 
which they are conceived or brought together in thought. 
We must not expect, for instance, when we endeavor to 
realize the Concept, Man, to find an object that is rational 
and animal, nothing more, nothing less ; — an object that 
is merely rational, with no attributes that determine this 
rationality more specifically — an object, for instance, that is 
not learned nor unlearned, prince nor savage ; that is not tall 
nor short, black nor white, male nor female. The Concept 
did not arise, was not formed, in such a way as to authorize 
any such expectation. It was founded immediately, as we 
have seen, in a plurality of judgments ; and these judgments 
were formed from what was presented to the thought. If 
this datum to the thought be, for example, supposed to have 
been presented by the Faculty of Perception, and the move- 
ment of Thought to have been from the whole to the parts, 
then, as we have seen, Thought took the datum as a whole, 
say Socrates, and one of its parts, say the composite attribute, 
rational animal, and affirmed this part of the whole, thus, 
Socrates is rational animal, leaving out of regard for the 
time, all other attributes or parts, as that he was learned, 
modest, tall, white, and the like. Other data, as Cicero, 
James, were presented and treated in the same way. Then 
these several judgments being thus in the mind, and having 
the same predicate, which was one of the many attributes 
originally given in the several subjects, Socrates, &c, were 
synthesized or aggregated, and the common predicate and 
copula being dropped, we attained the Concept, which we 
signalized in language as a unit, by the term Man. Now 
the only element of reality introduced by this process into 
the Concept is simply the attribute rational animal, given in 
the plurality of subjects, Socrates, Cicero, James. All of 
real, therefore, that we can expect to find in our endeavor 



68 PURE LOGIC. 

to realize the Concept, Man, is simply rational animal This 
complex attribute, if the Concept is valid, must be found, 
must be realized, in every subject embraced under the Con- 
cept in Socrates, Cicero, James, &c. ; but it would be absurd 
to expect more as necessarily expressed by the Concept, un- 
less the attribute under which as its necessary Base the Con- 
cept was formed as being identical in the plurality of subjects, 
embraced something more than rational animal. 

Inasmuch as words expressing Concepts make up a great 
majority of the terms in use in language, it becomes an in- 
teresting question, how far and on what grounds we may 
assume such words to denote real objects. And, although 
the question in its full import transcends the proper sphere 
of logical science, yet as the exposition we have given of the 
genesis of the Concept enables us to indicate the conditions 
of such a correspondence, and as some knowledge of them is 
necessarily involved in logical methodology, where the ques- 
tion will again meet us, it may be proper here in a very sum- 
mary way to indicate them. 

1. The original datum to thought must be a true presenta- 
tion of the real object, and this implies two things : (1) 
that objective reality may be apprehended by the human 
mind ; and (2) that the mind rightly apprehends it. 

2. The objective world must have in its parts likenesses 
or resemblances corresponding to the identities recognized in 
forming the Concept. This condition implies (1) that the 
objective world has parts corresponding to those apprehended 
in thought ; (2) that these parts are in some respects identi- 
cal one with another ; and (3) that the identities recognized 
in Thought, in the Concept, are the same as those that exist 
in the real objects of thought. 

In all thinking, and especially in all communication of 
thought, in all discourse, there are three elements which it is 
ever necessary to discriminate with careful vigilance. There 
are, first, the objects of which we think or speak ; secondly, 
our cognitions or mental apprehensions of those objects ; and, 



CONCEPTS. 69 

thirdly, the words in which these cognitions of these objects 
of our thought are expressed. Thought thus stands in a 
twofold relation to its object, and to its expression or embodi- 
ment ; and there is accordingly a twofold liability to error, 
as we may, in the first place, confound our thoughts, our 
cognitions, with the objects of which we think ; or, in the 
second place, confound these cognitions with the words in 
which they are expressed. 

In respect to this second relation of thought, its relation 
to language, their reciprocal dependence on each other, and 
the imperfection of thought by reason of this dependence, 
the following general observations of Sir William Hamilton 
are particularly worthy of attention : — 

" For Perception, indeed, for the mere consciousness of 
the similarities and dissimilarities in the objects perceived, 
for the apprehension of the causal connection of certain 
things, and for the application of this knowledge to the at- 
tainment of certain ends, no language is necessary; and it is 
only the exaggeration of a truth into an error, when philos- 
ophers maintain that language is the indispensable condition 
of even the simpler energies of knowledge. Language is 
the attribution of signs to our cognitions of things. But as 
a cognition must have been already there, before it could re- 
ceive a sign, consequently that knowledge which is denoted 
by the formation and application of a word must have pre- 
ceded the symbol which denotes it. Speech is thus not the 
mother, but the godmother, of knowledge. But though, in 
general, we must hold that language, as the product and cor- 
relative of thought, must be viewed as posterior to the act 
of thinking itself; on the other hand, it must be admitted, 
that we could never have risen above the very lowest de- 
grees in the scale of thought, without the aid of signs. A 
sign is necessary to give stability to our intellectual progress 
— to establish each step in our advance as a new starting- 
point for our advance to another beyond. 

" A country may be overrun by an armed host, but it is 



70 PURE LOGIC. 

only conquered by the establishment of fortresses. Words 
are the fortresses of thought. They enable us to realize our 
dominion over what we have already overrun in thought ; to 
make every intellectual conquest the basis of operations for 
others still beyond. Or another illustration : All have heard 
of the process of tunneling, of tunneling through a sand- 
bank. In this operation it is impossible to succeed, unless 
every foot, nay almost every inch in our progress, be secured 
by an arch of masonry, before we attempt the excavation of 
another. Now, language is to the mind precisely what the 
arch is to the tunnel. The power of thinking and the power 
of excavation are not dependent on the word in the one case, 
or the mason-work in the other ; but jvithout these subsidia- 
ries, neither process could be carried on beyond its rudiment- 
ary commencement. Though, therefore, we allow that every 
movement forward in language must be determined by an 
antecedent movement forward in thought ; still, unless thought 
be accompanied at each point of its evolution by a corre- 
sponding evolution of language, its further development is 
arrested. Thus it is, that the higher exertions of the higher 
faculty of Understanding — the classification of the objects 
presented and represented by the subsidiary powers in the 
formation of a hierarchy of notions, the connection of these 
notions into judgments, the inference of one judgment from 
another, and, in general, all our consciousness of the rela- 
tions of the universal to the particular, consequently all 
science strictly so denominated, and every inductive knowl- 
edge of the past and future from the laws of nature — not 
only these, but all ascent from the sphere of sense to the 
sphere of moral and religious intelligence, are, as experience 
proves, if not altogether impossible without a language, at 
least possible to a very low degree. 

" Admitting even that the mind is capable of certain ele- 
mentary concepts without the fixation and signature of lan- 
guage, still these are but sparks which would twinkle only to 
expire ; and it requires words to give them prominence, and, 



CONCEPTS. 71 

by enabling us to collect and elaborate them into new con- 
cepts, to raise out of what would otherwise be only scattered 
and transitory scintillations a vivid and enduring light. 

"As a notion or concept is the factitious whole or unity 
made up of a plurality of subjects or of attributes — a whole 
too often of a very complex multiplicity ; and as this multi- 
plicity is only mentally held together, inasmuch as the con- 
cept is fixed and ratified in a sign or word ; it frequently 
happens that, in its employment, the word does not suggest 
the whole amount of thought for which it is the adequate 
expression, but, on the contrary, w r e frequently give and take 
the sign, either with an obscure or indistinct consciousness of 
its meaning, or even without an actual consciousness of its 
signification at all. In consequence of this, when a notion is 
of a very complex and heterogeneous composition, we are 
frequently w r ont to use the term by which it is denoted, with- 
out a clear or distinct consciousness of the various characters 
of which the notion is the sum ; and thus it is, that we both 
give and take words without any, or, at least, without the 
adequate complement of thought. In countries where bank- 
notes have not superseded the use of the precious metals, 
large payments are made in bags of money, purporting to 
contain a certain number of a certain denomination of coin, 
or, at least, a certain amount in value. Now, these bags are 
often sealed up and passed from one person to another, with- 
out the tedious process, at each transference, of counting out 
their contents, and this upon the faith that, if examined, they 
will be found actually to contain the number of pieces for 
which they are marked, and for which they pass current. 
In this state of matters, it is, however, evident, that many 
errors or frauds may be committed, and that a bag may be 
given and taken in payment for one sum, which contains 
another, or which, in fact, may not even contain any money 
at all. Now the case is similar in regard to notions. As the 
sealed bag or rouleau testifies to the enumerated sum, and 
gives unity to what would otherwise be an unconnected mul- 



72 PURE LOGIC. 

titude of pieces, each, only representing its separate value ; so 
the sign or word proves and ratifies the existence of a concept, 
that is, it vouches the tying up of a certain number of at- 
tributes or characters in a single concept — attributes which 
would otherwise exist to us only as a multitude of separate 
and unconnected representations of value. So far the anal- 
ogy is manifest ; but it is only general. The bag, the guar- 
anteed sum, and the constituent coins, represent in a still 
more proximate manner the term, the concept, and the con- 
stituent characters. For in regard to each, we may do one 
of two things. On the one hand, we may test the bag, that 
is, open it, and ascertain the accuracy of its stated value, by 
counting out the pieces which it purports to contain ; or we 
may accept and pass the bag, without such a critical enumer- 
ation. In the other case, we may test the general term, 
prove that it is valid for the amount and quality of thought 
of which it is the sign, by spreading out in consciousness the 
various characters of which the concept professes to be the 
complement; or we may take and give the term without 
such an evolution. 

" It is evident from this, that notions or concepts are pecu- 
liarly liable to great vagueness and ambiguity, and that their 
symbols are liable to be passed about without the proper kind, 
or the adequate amount, of thought." 

§ 40. Inasmuch, likewise, as a Concept is in its essential 
a Concept is nature an aggregate resulting from the synthesis 
a Quantity. f ^ e subjects or of the predicates in several Judg- 
ments, it is necessarily to be regarded as a Quantity. And 
in this, its most essential characteristic, we are to find the 
highest principle of Division in the distribution of Concepts. 
But inasmuch as a Concept may be a synthesis of Subjects or 
of Predicates, we have at once given us the primary distinc- 
tion of Concepts into the two classes of Subject-Concepts and 
Predicate-Concepts. These two kinds of Quantity have been 
denominated by logicians Extensive Quantity and Compre- 
hensive or Intensive Quantity ; Extensive Quantity belong- 



CONCEPTS. 73 

ing to concepts in so far as formed of subjects, and Compre- 
hensive Quantity belonging to them in so far as they are 
formed of predicates. 

§ 41. The Extensive Quantity of a concept, other- 
wise called its Extension, also its sphere or domain, Extensive 
sphcera, regio, quantitas, ambitus, and by the Q uantifc y- 
Greek logicians, its breadth or latitude, 7rAaTos, respects the 
concept as a complement of subjects. Thus the concept, 
man, taken in its Extensive Quantity, denotes the aggregate 
of the individual subjects of which some common attributes 
may have been predicated in Judgments actually or impliedly 
made before, as Socrates, Cicero, James, and all other indi- 
viduals judged as rational animal. 

In this Quantity the relation of the concept as a whole to 
the particular subjects which are its component parts, is ex- 
pressed by the preposition under ; thus, Socrates is said to 
be contained under the concept, man. 

§ 42. The Comprehensive Quantity of a concept, 
otherwise called its Intensive or Internal Quan- compreheu- 
tity, its Comprehension, Intension, quantitas com- tensive 3 *" 
plexus, also by the Greek logicians depth, /3d0os, °- uantit y- 
respects the concept as a complement of predicates or attri- 
butes ; as thus the concept, man, taken in its Comprehensive 
Quantity, denotes the aggregate of the attributes that may 
have been predicated of the same subject in former actual or 
implied Judgments, as rational and animal, attributed sever- 
ally to the same subject, Socrates. 

In this Quantity, the relation of the concept as a whole 
to the particular attributes which are its component parts, is 
expressed by the preposition in ; thus the concept, man, is 
said to contain in it the attribute rational. 

§ 43. Nothing in the formation of a concept forbids a 
synthesis of terms that are themselves concepts. 

rni ... , . . . -r , Amplifica- 

lhe primitive concepts, as the primitive Judg- tion of Con- 
ments, must be of terms that are individual ; but cep s ' 
these terms may be combined with other individual terms or 



74 PURE LOGIC. 

with concepts, or concepts may be combined with other con- 
cepts, and in either quantity, the Base ever remaining un- 
changed. 

The logical process by which a term is amplified by being 
combined with other analogous terms, if in Extensive Quan- 
tity, is called Generalization ; if in Comprehensive Quantity, 
it is called Determination. 

This process of amplifying a term or concept, may be thus 
exemplified. We will begin with a primitive consciousness in 
which an object of sight, say the Moon, is brought into it. 
The Judgment, when this cognition given by the Faculty of 
Perception and the Intuitive Cognition of Existence occa- 
sioned by the perception, present themselves before its view, 
at once affirms Existence both of the subject perceiving — 
the Ego — and also of the object perceived, I am, The moon 
is, the verb being used here substantively to include both the 
copula and the predicate of Existence. Under the common 
predicate, the subjects may be synthesized, and a concept 
emerges, which, by successive syntheses of subjects, becomes 
the concept being, comprehending all objects of Thought 
which agree in respect of this predicate. We can enlarge 
the contents of this concept taken in its Extensive Quantity, 
by bringing into it or under it any other subject of a Judg- 
ment having this predicate ; but we can add no existing 
subject to Being so as to form a higher class of subjects. 
We cannot, therefore, amplify the concept being, so that it 
shall become a higher genus. The limit to the amplification 
of a subject-concept, that is, of a concept in Extensive 
Quantity, is thus a perfectly simple predicate. But this 
predicate may be amplified if we find a subject having this 
and some other predicate. Thus in the Judgments The Moon 
is existing, The Moon is material, by combining the predicates 
there emerges the predicate-concept Material Existence, that 
is, Matter. We may go on to amplify this concept, taken in 
Comprehensive Quantity, by combining with it under some 
common subject another predicate, as luminous, and, still 



CONCEPTS. 75 

further, by adding to this new amplification, the predicate 
by reflection, till we reach the limit of amplification in this 
direction. It is obvious that as we thus amplify the com- 
prehension of the concept, we are contracting the bounda- 
ries of the subject of which the concept may be affirmed, that 
is, we are determining it. Thus existence may be predi- 
cated of many objects ; material, of fewer ; luminous, of fewer 
still ; luminous by reflection, of yet fewer objects. The proc- 
ess of amplifying the comprehension is called, therefore, 
Determination, as logical nomenclature has originated rather 
from the view of objects in their Extensive Quantity. It is 
also called Concretion. 

On the other hand, if we begin with a subject having not 
a simple predicate as before, but one more or less amplified, 
we may amplify the Extension of this subject by combining 
with it subjects having some part of this predicate in common. 
Thus beginning with Socrates in any Judgment having a 
predicate not absolutely simple, as in the Judgment, Socrates 
is of Athens, we may add subjects in Judgments having the 
same predicate, as, Plato is of Athens, Alcibiades is of Athens, 
Xenophon is of Athens, &c, and we obtain the subject-concept 
Athenian, embracing under it many individuals. So, again, 
by combining Athenian, Theban, Spartan, under the common 
predicate of Greece or Grecian, we amplify the Extension still 
more, that is, we bring more subjects under it. This proc- 
ess, that of amplifying the Extension, is called Generaliza- 
tion. 

It will be observed that, from the inadequacy of language 
to signalize all the modifications of Thought, these two quan- 
tities, notwithstanding they differ so much, are not always 
distinguished by peculiar forms of verbal expression. Indeed, 
almost every term may be used indifferently either as Subject 
or as Predicate, and accordingly in either Comprehension or 
Extension. The use in discourse alone can ordinarily indi- 
cate in which Quantity the term is used. Individuals, as 
such, can never, indeed, be predicates, except in Identical 



76 PURE LOGIC. 

Propositions; yet Language does not hesitate at its will to 
trample upon this high prerogative of individuality, and con- 
script it into the ranks of its predicates, as its wants require. 
It makes Alexander to serve as predicate of every ambitious 
military conqueror, and proceeds thus to create a genus of 
Alexanders — restoring the subject-character, but robbing it 
of the individual prerogative. Hence the necessity to correct 
and valid Thought of a careful discrimination of this twofold 
significance of a term denoting a concept. 

The ability to be acquired only by intelligent practice, 
readily, and, as it w r ere, instinctively, to distinguish these two 
quantities in the import of concepts, is needed in order to the 
ready and correct interpretation of discourse ; to facile criti- 
cism of discourse, also, and determination of its conformity to 
truth, and the detection and exposure of error. Discourse, 
moreover, becomes at once freighted with a double richness 
of meaning to the mind practiced and skillful in this discrim- 
ination. But vastly more needful is this dexterity in the 
construction of Discourse. In this the main and more essen- 
tial labor consists in the right unfolding of knowledge, which 
for the most part is laid up in concepts. To unfold concepts 
in ignorance of their twofold quantity is not only difficult and 
slow, because in blindness as to the necessary path to be pur- 
sued, but, also, unavoidably liable to confusion, from which it 
has bfeen truly said it is more difficult for truth to emerge 
than from absolute error. 

It is pertinent to remark in this connection that obviously 
common nouns, or, as they might more properly be called, 
class nouns, are as really abstractions as any others. They 
do not stand for any actual concrete realities. There is, as 
has been shown, no real being answering to the concept horse, 
having the characters solid-hoofed, non-ruminant, mammal, 
and no others. The concept is a mere product of Thought, 
and is the result of abstraction. It is only by abstracting 
from other properties or characters, and thus limiting the 
attention to one or more, that we can form a thought of any 



CONCEPTS. 77 

class of subjects. Thus it happens, that any predicate, as it 
can be made a subject in a Judgment, so can be a class noun. 
A concrete noun can differ from an abstract only in this re- 
spect, that in its use it is treated as a Subject-concept, while 
an abstract noun is treated as a predicate-concept. 

" Such, in general, is what is meant by the two quantities 
of concepts — their Extension and Comprehension. 

§ 44. u But these quantities are not only different, they are 
opposed, and so opposed, that though each supposes intensive 
the other as the condition of its own existence, still, ^ Q^anti- 
however, within the limits of conjunct, of correl- j^f 1 ^ ° P ~ 
ative existence, they stand in an inverse ratio to eacn other - 
each other — the maximum of the one being the minimum 
of the other. 

"A notion is extensively great in proportion to the greater 
number, and extensively small in proportion to the smaller 
number of subjects it contains under it. When the Exten- 
sion of a concept becomes a minimum, that is, when it con- 
tains no other notions under it, it is called an individual. 

"A notion is intensively great in proportion to the greater 
number, and intensively small in proportion to the 

-, . ., ^aw regulat- 

smaller number of determinations or attributes ing tnemut- 
contained in it. Is the Comprehension of a con- tions of Ex- 

, • • tx . • « ,i . • tension and 

cept a minimum, that is, is the concept one in comprehen- 
which a plurality of attributes can no longer be S10n * 
distinguished, it is called simple ; whereas, inasmuch as its 
attributes still admit of discrimination, it is called complex or 
compound. 

" These two quantities stand always in an inverse ratio to 
each other : for the greater the Comprehension of a concept, 
the less is its Extension ; and the greater its Extension the 
less its Comprehension. 

" When I take out of a concept, that is, abstract from it one 
or more of its attributes, I diminish its comprehen- 

mi i n ,i , • Illustration. 

sion. lhus, when from the concept, maw, equiva- 



78 PURE LOGIC. 

lent to rational animal, I abstract the attribute or determi- 
nation rational, I lessen its internal quantity. But by this 
diminution of its comprehension I give it a wider extension ; 
for what remains is the concept, animal, and the Concept 
animal embraces under it a far greater number of subjects 
than the concept man" 

§ 45. Concepts have been characterized by certain relations 
which they bear to one another. The most im- 

Reciprocal ' •f . . 

Relations of portant of the different kinds of concepts as thus 
determined will best be exhibited separately under 
the two kinds of Quantity. 

"As dependent upon Extension, concepts stand to each 
Under Ex- other in the live mutual relations : 1°. Of Exclu- 
tension. s j on . 2°. Of Coextension ; 3°. Of Subordination ; 
4°. Of Coordination ; and 5°. Of Intersection. 

" 1. One concept excludes another when no part of the 
one coincides with any part of the other. 2. One concept is 
coextensive with another, when each has the same subordi- 
nate concepts under it. 3. One concept is subordinate to 
another (which may be called the Super ordinate) when the 
former is included within, or makes a part of, the sphere or 
extension of the latter. 4. Two or more concepts are coor- 
dinated, when each excludes the other from its sphere, but 
when both go immediately to make up the extension of a 
third concept, to which they are co-subordinate. 5. Concepts 
intersect each other, when the sphere of the one is partially 
contained in the sphere of the other. 

" Of Exclusion, horse, syllogism, are examples : there is no 
absolute exclusion. 

" As examples of Coextension — the concepts living being, 
Examples of and organized being, may be given. For, using 
uai relations" tne term life as applicable to plants as well as ani- 
^nExt^n- 6 ^ 8 ma H there is nothing living which is not organ- 
sion. ized, and nothing organized which is not living. 

This reciprocal relation will be represented by two circles 
covering each other, or by two lines of equal length and in 
positive relations. 



CONCEPTS. 79 

"As examples of Subordination and Coordination — man, 
dog, horse, stand, as correlatives, in subordination to the con- 
cept animal, and, as reciprocal correlatives, in coordination 
with each other. 

"What is called the reciprocal relation of Intersection, 
takes place between concepts when their spheres cross or cut 
each other, that is, fall partly within, partly without each 
other. Thus, the concept black and the concept heavy mu- 
tually intersect each other, for of these some black things 
are heavy, some not, and some heavy things are black, some 
not. 

" Of these relations, those of Subordination and Coordina- 
tion are of principal importance, as on them reposes the 
whole system of classification ; and to them alone it is, there- 
fore, necessary to accord a more particular consideration. 

" Under the Subordination of notions, there are various 
terms to express the different modes of this relation ; these it 
is necessary to bear in mind, for they form an essential part 
of the language of Logic, and will come frequently, in the 
sequel, to be employed in considering the analysis of Reason- 



ings. 



§ 46. " Of notions which stand to each other in the rela- 
tions of Subordination — the one is the Higher or H 

° Superior and 

Superior (notio, conceptus, superior), the other the interior, 
Lower or Inferior (notio, conceptus, inferior). Narrower, 
The superior notion is likewise called the Wider 
or Broader (latior), the inferior is likewise called the Nar- 
rower (angustior). 

" A notion is called the higher or superior, inasmuch as it 
is viewed as standing over another in the relation of subor- 
dination — as including it within its domain or sphere ; and 
a correlative notion is called the lower or inferior, as thus 
standing under a superior. Again, the higher notion is called 
the wider or broader, as containing under it a greater num- 
ber of things ; the lower is called the narrower, as contain- 
ing under it a smaller number. 



80 PURE LOGIC. 

" The higher or wider concept is called, also, in contrast to 
w . the lower or narrower, a Universal or General 

and Particu- Notion (vorjfxa kol66\ov, notio, conceptus, universa- 

lar Notions. ,. T . N . , . . 

/zs, generalis) ; the lower or narrower concept, in 
contrast to the higher or wider, a Particular Notion (vorjixa 
fieptKov, notio, conceptus, particulars) . 

"A notion is called universal, inasmuch as it is considered 
as binding up a multitude of parts or inferior concepts into 
the unity of a whole ; for universus means in unum versus, 
or ad unum versus, that is, many turned into one, or many 
regarded as one, and universal is employed to denote the 
attribution of this relation to objects. A notion is called 
particular, inasmuch as it is considered as one of the parts of 
a higher concept or whole. 

"A superior concept is also called a General Notion (votj/jlol 
Genus and KaOokov, notio, conceptus, generalis), or, in a single 
Species. word, a Genus (yeVos, genus) : and an inferior 

concept, contained under a higher, is called a Special Notion 
(vorjfjLa €l8lk6v, notio, conceptus, specialis), or, in a single word, 
a Species (eTSos, species). The abstraction which carries up 
species into genera, is called, in that respect, Generalization. 
The determination which divides a genus into its species is 
called, in that respect, Specification. Genera and Species 
are both called Classes ; and the arrangement of things under 
them is, therefore, Classification. 

" It is manifest that the distinction into Genera and Spe- 
m „. ± . cies is a merely relative distinction ; as the same 

The distmc- . . . . 

tion of Genus notion is, in one respect, a genus, in another re- 

and Species . . 

merely reia- spect, a species. h or except a notion has no 
higher notion, that is, except it be itself the widest 
or most universal notion, it may always be regarded as sub- 
ordinated to another ; and, in so far as it is actually thus re^- 
garded, it is a species. Again, every notion, except that 
which has under it only individuals, is, in so far as it is 
thus viewed, a genus. For example, the notion, triangle, 
if viewed in relation to the notion of rectilineal figure, is a 



CONCEPTS. 81 

species, as is likewise rectilineal figure itself, as viewed in 
relation to figure simply. Again, the concept triangle is a 
genus, when viewed in reference to the concepts — right- 
angled triangle, acute-angled triangle, etc. A right-angled 
triangle is, however, only a species, and not possibly a genus, 
if under it be necessarily included individuals alone. But, 
in point of fact, it is impossible to reach in theory any lowest 
species; for we can always conceive some difference by 
which any concept may be divided ad infinitum. This, how- 
ever, as it is only a speculative curiosity, like the infinites- 
imal divisibility of matter, may be thrown out of view in re- 
lation to practice ; and, therefore, the definition, by Porphyry 
and logicians in general, of the lowest species, is practically 
correct, even though it cannot be vindicated against theoret- 
ical objections. On the other hand, we soon and easily reach 
the highest genus, which is given in to ov, ens aliquid, being, 
thing, something, etc., which are only various expressions of 
the same absolute universality. 

K In regard to the terms Generalization and Specification, 
these are limited expressions for the processes of Generifica- 
Abstraction and Determination, considered in a s™ ci a fi C ation 
particular relation. And first, in regard to Ab- ~~ what - 
straction and Generification. In every complex notion, we 
can limit our attention to its constituent characters, to the ex- 
clusion of some one. We thus think away from this one — 
we abstract from it. Now, the concept which remains, that 
is, the fasciculus of thought minus the one character which 
we have thrown out, is in relation to the original — the entire 
concept, the next higher — the proximately superior notion. 
But a concept and a next higher concept are to each other as 
species and genus. The process of Abstraction, therefore, 
by which out of a proximately lower, we evolve a proxi- 
mately higher, concept, is, when we speak with logical pre- 
cision, called the process of Generalization. 

" Take, for example, the concept, man. This concept is 
proximately composed of the two concepts or constituent 
6 



82 PURE LOGIC. 

characters — animal and rational being. If we think either 
of these characters away from the other, we shall have in 
that other a proximately higher concept, to which the con- 
cept man stands in the relation of a species to its genus. 
If we abstract from animal, then man will stand as a species 
in subordination to the genus, rational being, and the concept, 
animal, will then afford only a difference to distinguish man 
as a coordinate species from immaterial intelligences. If, on 
the other hand, we abstract from rational being, then man 
will stand as a species in subordination to the genus animal, 
having for a coordinate species, irrational animal. Such is 
the process of Generalization. Now for the converse process 
of Specification. 

" Every series of concepts which has been obtained by 
abstraction, may be reproduced in an inverted order, when, 
descending from the highest notion, we step by step add on 
the several characters from which we had abstracted in our 
ascent. This process, as has been stated, is called Determi- 
nation — a very appropriate expression, inasmuch as by each 
character or attribute which we add on, we limit or deter- 
mine, more and more, the abstract vagueness or extension of 
the notion ; until, at last, if every attribute be annexed, the 
sum of attributes contained in the notion becomes convertible 
with the sum of attributes of which some concrete individual 
or reality is the complement. Now, when we determine any 
notion by adding on a subordinate concept, we divide it ; for 
the extension of the higher concept is precisely equal to the 
extension of the added concept plus its negation. Thus, if 
to the concept, animal, we add on the next lower concept, 
rational, we divide its extension into two halves — the one 
equal to rational animal, the other equal to its negation, 
that is, to irrational animal. Thus an added concept and its 
negation always constitute the immediately lower notion, into 
which a higher notion is divided. But as a notion stands to 
the notions proximately subordinate to it in the immediate 
relation of a genus to its species, the process of Determina- 



CONCEPTS. 83 

tion, by which a concept is thus divided, is, in logical lan- 
guage, appropriately denominated Specification. 

" So much in general for the Subordination of notions, 
considered as Genera and Species. There are, however, 
various gradations of this relation, and certain terms by 
which these are denoted. The most important of these are 
comprehended in the following paragraph. 

§ 47. " A Genus is of two degrees — a highest and a lower. 
In its highest degree, it is called the Supreme or 

CrradatlOIlS 

Most General Genus (vivos yzviKUTarov, genus sum- of Genera 

and Species 

mum, or generalissimum), and is defined, 'that and their 

, . , , . , , , designations. 

which being a genus cannot become a species. 
In its lower degree, it is called a Subaltern or Intermediate 
(yeVos viraXXrqXov, genus subalternum or medium), and is de- 
fined, ' that which being a genus can also become a species.' 
A Species, also, is of two degrees — a lowest and a higher. 
In its lowest degree, it is called a Lowest or Most Special 
Species (etSos ctStKwrarov, species infima, ultima, or specialis- 
sima), and is defined, ' that which being a species cannot be- 
come a genus.' In its higher degree, it is called a Subaltern 
or Intermediate Species (eTSos v7rdWr]\ov, species subalterna 
media), and is defined, 'that which being a species may also 
become a genus.' Thus a Subaltern Genus and a Subaltern 
Species are convertible. 

" These distinctions and definitions are taken from the cele- 
brated Introduction of Porphyry to the Categories of Aris- 
totle, and they have been generally adopted by logicians. It 
is evident that the only absolute distinction here established 
is that between the Highest or Supreme Genus and the Low- 
est Species ; for the other classes — to wit, the Subaltern 
or Intermediate — are, all and each, either genera or species, 
according as we regard them in an ascending or a descending 
order — the same concept being a genus, if considered as a 
whole containing under it inferior concepts as parts, and a 
species, if considered as itself the part of a higher concept or 
whole. The distinction of concepts into Genus and Species, 



84 PURE LOGIC. 

into Supreme and Intermediate Genus, into Lowest and Inter- 
mediate Species, is all that Logic takes into account ; because 
these are all the distinctions of degree that are given neces- 
sarily in the form of thought, and as abstracted from all de- 
terminate matter. 

" It may be remarked, by the way, that in the physical 
sciences of arrangement, the best instances of which are 
seen in the different departments of Natural History, it is 
found necessary, in order to mark the relative place of each 
step in the ascending and descending series of classes, to 
bestow on it a particular designation. Thus kingdom, sub- 
kingdom, class, order, tribe, family, genus, subgenus, species, 
subspecies, variety, and the like, are terms that serve conven- 
iently to mark out the various degrees of generalization, in 
its application to the descriptive sciences of nature. 
- § 48. " The character, or complement of characters, by 
Generic which a lower genus or species is distinguished, 

indMduaT d both ^ rom tne g enus to which it is subordinate, and 
Difference. f rom ^ e ther genera or species with which it is 
coordinated, is called the Generic or the Specific Difference, 
Scacj>opa yeviK-q, and Siac^opa etSi/oy, differentia generica, and 
differentia specijica. The sum of characters, again, by which 
a singular or individual thing is discriminated from the spe- 
cies under which it stands and from other individual things 
along with which it stands, is called the Individual or Sin- 
gular or Numerical Difference (differentia individualis vel 
singularis vel numerica). 

" Two things are thus said to be generically different, inas- 
much as they lie apart in two different genera ; 

Generic and it 

Specific Dif- specifically different, inasmuch as they lie apart in 
two different species ; individually or numerically 
different, inasmuch as they do not constitute one and the 
same reality. Thus, animal and stone may be said to be 
generically different ; horse and ox to be specifically different ; 
Highflyer and Eclipse to be numerically or individually dif- 
ferent. It is evident, however, that as all genera and species, 



CONCEPTS. 85 

except the highest of the one and the lowest of the other, may 
be styled indifferently either genera or species, generic differ- 
ence and specific difference are in general only various ex- 
pressions of the same thing; and, accordingly, the terms 
heterogeneous and homogeneous, which apply properly only to 
the correlation of genera, are usually applied equally to the 
correlation of species. 

u Individual existence can only be perfectly discriminated 
in Perception, external or internal, and their nu- „,,..: , 

r 7 . Individual 

merical differences are endless ; for of all possible or singular 
contradictory attributes, the one or the other must, 
on the principles of Disjunction and Excluded Middle, be 
considered as belonging to each individual thing. On the 
other hand, species and genera may be perfectly discrimi- 
nated by one or few characters. For example, man is dis- 
tinguished from every genus or species of animal by the one 
character of rationality ; triangle, from every other class of 
mathematical figures, by the single character of trilaterality. 
It is, therefore, far easier adequately to describe a genus or 
species than an individual existence; as in the latter case 
we must select, out of the infinite multitude of characters 
which an individual comprises, a few of the most prominent, 
or those by which the thing may most easily be recognized. 
But as those which we thus select are only a few, and are 
only selected with reference to our faculty of apprehension 
and our capacity of memory, they always constitute only a 
petty, and often not the most essential part of the numerical 
differences by which the individuality of the object is de- 
termined. 

§ 49. " Notions, in so far as they are considered the coor- 
dinate species of the same genus, may be called .. 
Conspecies ; and in so far as Conspecies are con- tion of Con- 
sidered to be different but not contradictory, they 
are properly called Discrete or Disjunct Notions (notiones 
discretes vel disjunctce). 

§ 50. " The whole classification of things by Genera and 



86 PURE LOGIC. 

Species is governed by two laws. The one of these, the law 
The two gen- of Homogeneity (principium Hbmogeneitatis), is 
which Suh- — That how different soever may be any two con- 
and cobrdi- cepts, they both still stand subordinated under 
derExten- some higher concept ; in other words, things the 
Sated— reS " most dissimilar must, in certain respects, be simi- 
viz., of Ho- j ar# The other, the law of Heterogeneity (prin- 

mogeneity ' v a \L 

andHetero- cipium Heterogeneitatis) , is — That every concept 
contains other concepts under it ; and, therefore, 
when divided proximately, we descend always to other con- 
cepts, but never to individuals ; in other words, things the 
most homogeneous — similar — must, in certain respects, be 
heterogeneous — dissimilar. 

" Of these two laws, the former, as the principle which en- 
ables, and in fact compels, us to rise from species to genus, is 
that which determines the process of Generification ; and the 
latter, as the principle which enables, and in 'fact compels, us 
to find always species under a genus, is that which regulates 
the process of Specification. The second of these laws, it is 
evident, is only true ideally, only true in theory. The infin- 
ite divisibility of concepts, like the infinite divisibility of space 
and time, exists only in speculation. And that it is theoret- 
ically valid, will be manifest, if we take two similar concepts, 
that is, two concepts with a small difference : let us then 
clearly represent to ourselves this difference, and we shall 
find that how small soever it may be, we can always conceive 
it still less, without being nothing, that is, we can divide it ad 
infinitum ; but as each of these infinitesimally diverging dif- 
ferences affords always the condition of new species, it is 
evident that we can never end, that is, reach the individual, 
except per saltum. 

§ 51. " When two or more concepts are compared together 
identical according to their Comprehension, they either co- 

and Different . " . - , -, f . , . , ; 

Notions. incide or they do not ; that is, they either do or do 
not comprise the same characters. Notions are thus divided 
into Identical and Different (conceptus identici et diversi). 



CONCEPTS. 87 

The Identical are either absolutely or relatively the same. 
Of notions Absolutely Identical there are actually none ; no- 
tions Relatively Identical are called, likewise, Similar or Cog- 
nate (notiones similes, affines, cognates) ; and if the common 
attributes, by which they are allied, be proximate and neces- 
sary, they are called Reciprocating or Convertible (notiones 
reciprocce, convertibiles). 

" In explanation of this paragraph, it is only necessary to 
say a word in regard to notions absolutely Identi- Absolutely 
cal. That such are impossible, is manifest. For, it Notions im- 
being assumed that such exist, as absolutely iden- P 0SSlble - 
tical, they necessarily have no differences by which they can 
be distinguished : but what are indiscernible can be known, 
neither as two concepts nor as two identical concepts ; be- 
cause we are, ex hypothesi, unable to discriminate the one 
from the other. They are, therefore, to us as one. Notions 
absolutely identical can only be admitted, if, abstracting our 
view altogether from the concepts, we denominate those no- 
tions identical which have reference to one and the same 
object, and w T hich are conceived either by different minds, or 
by the same mind, but at different times. Their difference is, 
therefore, one not intrinsic and necessary, but only extrinsic 
and contingent. Taken in this sense, Absolutely Identical 
notions will be only a less correct expression for Reciprocat- 
ing or Convertible notions. . 

§ 52. " Considered under their Comprehension, concepts, 
again, in relation to each other, are said to be opposition 
either Congruent or Agreeing, inasmuch as they ofConce P ts - 
may be connected in thought ; or Conflictive, inasmuch as 
they cannot. The connection constitutes the Opposition of 
notions (to olvt lk€lo-6 at, oppositio). This is twofold : 1°. 
Immediate or Contradictory Opposition, called likewise Re- 
pugnance (TO OLVTicjiaTLKOiS CLVTlKU&OcLL, aVTL<f>CL<rLS, OppOSitio 

immediata sive contradictoria, repugnantia) ; and, 2°. Me- 
diate or Contrary Opposition (to cvavrtcos avTiKdo-Oai, kvav- 
tlottjs, oppositio mediata vel contraria). The former emerges 



88 PURE LOGIC. 

when one concept abolishes (tollit), directly or by simple 
negation, what another establishes (ponit) ; the latter, when 
one concept does this not directly or by simple negation, but 
through the affirmation of something else. 

" Identity is not to be confounded with Agreement or Con- 
identity and g ruen ce, nor Diversity with Connection. All iden- 
Agreement; tieal concepts are, indeed, congruent; but all con- 
and Connie- gruent notions are not identical. Thus learning, 
and virtue, beauty and riches, magnanimity and 
stature, are congruent notions, inasmuch as, in thinking a 
thing, they can easily be combined in the notion we form of 
it, although in themselves very different from each other. In 
like manner, all conflicting notions are diverse or different no- 
tions, for unless different, they could not be mutually connect- 
ive, but on the other hand, all different concepts are not 
conflictive, but those only whose difference is so great that 
each involves the negation of the other; as, for example, 
virtue and vice, beauty and deformity, wealth and poverty. 
Thus these notions are by preeminence — /car e&^V — sa ^ 
to be opposed, although it is true that, in thinking, we can 
oppose, or place in antithesis, not only different, but even 
identical, concepts. 

" To speak now of the distinction of Contradictory and Con- 
Contradic- t r & r y Opposition, or of Contradiction and Contra- 
Contrar d o - rie ty ; of these the former, Contradiction, is exem- 
position. plified in the opposites — yellow, not yellow ; walk- 
ing, not walking. Here each notion is directly, immediately, 
and absolutely repugnant to the other — they are reciprocal 
negatives. This opposition is, therefore, properly called that 
of Contradiction or of Repugnance ; and the opposing no- 
tions themselves are contradictory or repugnant notions — in 
a single word, contradictories. The latter, or Contrary Op- 
position, is exemplified in the opposites, yellow, blue, red, etc., 
walking, standing, lying, etc. 

" In the case of Contradictory Opposition, there are only two 
conflictive attributes conceivable ; and of these one or other 



CONCEPTS. 89 

must be predicated of the object thought. In the case of 
Contrary Opposition, on the other hand, more than two con- 
nective characters are possible, and it is not, therefore, neces- 
sary, that if one of these be not predicated of an object, any 
one other must. Thus, though I cannot at once sit and 
stand, and consequently sitting and standing are attributes 
each severally incompatible with the other ; yet I may exist 
neither sitting nor standing — I may lie ; but I must either 
sit or not sit, I must either stand or not stand, etc. Such, 
in general, are the oppositions of Contradiction and Contra- 
riety." 

§ 53. Concepts as compared with each other in respect of 
their Comprehension, are further distinguished into intrinsic 
Intrinsic and Extrinsic. The former are made up Notlons - 
of those attributes which are presented to Thought as its view 
is turned from the object inwardly to its parts. These attri- 
butes are of the proper, inner being or essence of the object ; 
and, severally considered, are called Essentials, or Internal 
Denominations (ovcn^rj, essentialia, denominations internee, 
intrinsicce), and conjunctly, the Essence (ovvia, essentia). The 
latter, on the contrary, consist of those attributes which are 
presented to thought as its view is turned outward from the 
object to other objects around. These attributes of external 
relation are styled Accidents, or Extrinsic Denominations 
(crvju/^e^Kora, accidentia, denominationes externce or extrin- 
sicce). 

§54. " Further, in respect of their Comprehension, no 
less than of their Extension, notions stand to each involution 
other in a relation of Containing and Contained ; nation. 
and this relation, which, in the one quantity (extension) is 
styled that of Subordination, may in the other (comprehen- 
sion), for distinction's sake, be styled that of Involution. Co- 
ordination is a term w r hich may be applied in either quan- 
tity, being the relation alike in both of Part to Complementary 
Part. 

" In the quantity of comprehension, one notion is involved 



90 PUKE LOGIC. 

in another, when it forms a part of the sum total of charac- 
ters, which together constitute the comprehension of that other ; 
and two notions are in this quantity coordinated, when, while 
neither comprehends the other, both are immediately com- 
prehended in the same lower concept. 

" Thus the notion of the individual Socrates contains in it, 
besides a multitude of others, the characters of son of Soph- 
roniscus, Athenian, Greek, European, man, animal, organ- 
ized being, etc. But these notions, these characters, are not 
all equally proximate and immediate ; some are only given in 
and through others. Thus the character Athenian is appli- 
cable to Socrates only in and through that of son of Sophro- 
niscus — the character of Greek, only in and through that of 
Athenian — the character of European, only in and through 
that of Greek — and so forth ; m other words, Socrates is an 
Athenian only as the son of Sophroniscus, only a Greek as 
an Athenian, only a European as a Greek, only a man as a 
European, only an animal as a man, only an organized being 
as an animal. Those characters, therefore, that are given in 
and through others, stand to these others in relation of parts 
to wholes ; and it is only on the principle — Part of the part 
is a part of the whole, that the remoter parts are the parts 
of the primary whole. Thus, if we know that the individual 
Socrates comprehends the character son of Sophroniscus, and 
that the character son of Sophroniscus comprehends the char- 
acter Athenian ; we are then warranted in saying that Soc- 
rates comprehends Athenian, in other words, that Socrates 
is an Athenian. The example here taken is too simple to 
show in what manner our notions are originally evolved out 
of the more complex into the more simple, and that the prog- 
ress of science is nothing more than a progressive unfolding 
into distinct consciousness of the various elements compre- 
hended in the characters, originally known to us in their 
vague or confused totality." 



CHAPTER VI. 

THE PRODUCTS OF THOUGHT. III. REASONINGS. 

§ 55. The Third gradation of Thought is the Reasoning. 
Like the Concept, it is derived from the Judgment. Reason w — . 
It differs from the Concept in its form, as, unlike what lt is * 
that, it retains the full forms of the Judgment, and accord- 
ingly, also, to a certain extent, it differs from it in the mode 
of its derivation. It differs from the Judgment proper in 
this respect, that it is a derivation from a Judgment — a 
traced movement of Thought, superadded to that which con- 
stitutes the Judgment. It is not the derived Judgment, not 
the mere terminus, the point at the end of the line over which 
the Thought has moved, but the line itself as traced in the 
movement of the Thought. When viewed as a resultant prod- 
uct of Thought, therefore, it must be regarded as the track 
of Thought left marked by the movement, not the mere 
attained object or goal of the movement, which is nothing 
more than a Judgment. We are carefully to distinguish, 
therefore, a Reasoning from the Conclusion — from the Judg- 
ment which is attained by the reasoning. 

A Reasoning, thus, is a derivation of a Judgment from 
another Judgment or Judgments. 

§56. The term Reasoning is ambiguously employed to 
denote both the act, and, also, the product of the „ 

T -rv» • • Denomina- 

act. In its different gradations, this process of tions of the 

"DFOCGSS 

Thought has obtained a variety of other designa- 
tions, which may here for convenience be summarily enumer- 
ated and explained. 

" Considered as an act, Reasoning, or Discourse of Reason 



92 PURE LOGIC. 

(to Xoyi&o-Oai, Aoyt<r/xos, Sidvoia, to Siavoeurtfai), is, likewise, 
called the act or process of Argumentation (argumentation! s), 
of Ratiocination (ratiocinationis,) of Inference or Illation 
(infer endi), of Collecting (colligendi), of Concluding (con- 
cludendi), of Syllogizing (tov crvWoyc^eaOaL, barbarously syl- 
logisandi). The term Reasoning is likewise given to the 
product of the act ; and a reasoning in this sense (ratiocina- 
tio, ratiocinium) is likewise called an Argumentation (argu- 
mentation ; also, frequently, an Argument (argumentum), an 
Inference or Illation (illatio), a Collection (collectio), a Con- 
clusion (conclusion o~vfjL7ripacriJLa), and, finally, a Syllogism 
(crvWoy tcr/xos) . 

"Reasoning is a modification from the French raisonner 
whkSthe ( an< ^ tms a derivation fr° m tne Latin ratio), and 
process of corresponds to ratiocination which has indeed been 

Reasoning is x 7 

denominated, immediately transferred into our language under 
the form of ratiocination. Ratiocination denotes 

Reasoning. . 

Ratiocina- properly the process, but improperly, also, the 
product of reasoning ; Ratiocinium marks exclu- 
sively the product. The original meaning of ratio was 
computation, and from the calculation of numbers it was 
transferred to the process of mediate comparison in general. 

Discourse (discursus, hidvoia) indicates the opera- 
Discourse. « - • i i i i p 

tion ot comparison, the running backward and tor- 
ward between the characters or notes of objects (discurrerc 
inter notas, Siavo€icr0ai). The terms discourse and discursus, 
Bidvoia, are, however, often used for the reasoning process, 
strictly considered, and discursive is even applied to denote 
mediate, in opposition to intuitive, judgment, as is done by 
Milton. The compound term, discourse of reason, unambig- 
uously marks its employment in this sense. Arqu- 

Argumenta- ■ ■ . . 

tion. Argu- mentation is derived from argumentari, which 

ment. 

means argumentis uti ; argument again, argu- 
mentum — what is assumed in order to argue something — 
is properly the middle notion in a reasoning — that through 
which the conclusion is established ; and by the Latin Khet- 



REASONINGS. 93 

oricians it was defined, ' probabile inventum ad faciendam 
fldem. 9 It is often, however, applied as coextensive with 
argumentation. Inference or Illation (from in- 

Inference 

fero) indicates the carrying out into the last prop- 
osition what was virtually contained in the antecedent 
judgments. To conclude (concludere) , again, 
signifies the act of connecting and shutting into 
the last proposition the two notions which stood apart in the 
two first. A conclusion (conclusio) is usually 

, . . .„ Conclusion. 

taken, m its strict or proper signification, to mean 
the last proposition of a reasoning ; it is, sometimes, how- 
ever, used to express the product of the whole process. To 
syllogize means to form syllogisms. Syllogism To Syllogize 
(o-vAAoyioyxos) seems originally, like ratio, to have Syllogism. 
denoted a computation — an adding up ; and, like the greater 
part of the technical terms of Logic in general, was borrowed 
by Aristotle from the mathematicians. SuAAoytoyxos may, 
however, be considered as expressing only what the compo- 
sition of the word denotes — a collecting together ; for o-uAAo- 
yi&o-Oai comes from avXXeyetv, which signifies to collect 
Finally, in Latin, a syllogism is called collection 

-, 77. rS, • i n CollectiO. 

and to reason, colli gere. 1 his refers to the act of 
collecting, in the conclusion, the two notions scattered in the 
premises." 

§ 57. A Reasoning is composed of two parts — the origi- 
nal Judgment or Judgments which are the original integrant 
datum in the process, and the movement of the Reasoning. 
Thought in the process. As the datum is re- and^onse- 
garded as logically determining and preceding, it quent. 
is called the Antecedent, and the other part, regarded as logi- 
cally determined, or following, is called the Consequent. Its 
proper sign is therefore. These are the parts of a Reason- 
ing regarded as an Integrate Whole. 

§ 58. The Antecedent in a Reasoning may consist of a 
single Judgment, or of a plurality of Judgments. Divisions of 
If it consist of but one Judgment, the Reasoning ^Xdiafe- 1 
is called an Immediate Reasoning. If the ante- Mediate. 



94 PURE LOGIC. 

cedent consists of more than one Judgment, the Reasoning 
is called a Mediate Reasoning, or, more technically, a Syllo- 
gism. 

Again, in a Mediate Reasoning, the Antecedent may con- 

Syiiogism- s * st °^ tw0 > or °^ more ^ an tw0 > Judgments. In 
Sorites. the former case there emerges the Single Syllo- 

gism ; in the latter, the Poly syllogism, also called the Sorites. 

Still further, in a Mediate Reasoning the derived Judg- 
Cat ricai- ment may be mediated through the relations of 
Conditional, the terms contained in the Antecedent, or through 
those of the copulas — that is, the reasoning may turn on 
proper Concepts as wholes and parts in relations to each other, 
or on proper Judgments. In the former case, there emerges 
the Categorical Syllogism ; in the latter case, the so-called 
Conditional Syllogism. 

Once more, the reasoning may be fully expressed in the 
complete regular form of the Syllogism, or may 

T7t> •Httrm am a * * 

be Elliptical, one or other of the several Judg- 
ments which form it being suppressed and only implied. A 
reasoning in which one of the Judgments is thus suppressed, 
is called an Enihymeme. This is the more common form of 
a reasoning in actual discourse. Accordingly, Aristotle tells 
us that the Enthymeme is the Rhetorical Syllogism. 

An apparent relaxation of logical strictness characterizes 
this general division of Reasonings. It arises from the desire 
to retain the familiar nomenclature, while avoiding the error 
and confusion which attend it. Logicians have generally 
represented the Hypothetical and Disjunctive Syllogisms as 
differing from the Categorical in another respect than that 
here recognized. And this treatment has necessarily ob- 
scured and complicated the exposition of the proper charac- 
ters of the several species. No real difficulty will, however, 
follow our continuing the old denominations ; but certain ex- 
planations of the names will differ from those to be found in 
previous logical treatises. 

§ 59. An Immediate Reasoning is an immediate deri- 



REASONINGS. 95, 

vation of a Judgment from another single Judg- Immediate 
ment ; as, Man is rational animal ; therefore, Man Reasonings. 
is rational. 

The occasions and objects of our thinking often demand 
that the form of an attained Judgment be changed, so that 
the primitive Judgment shall be treated as a datum, or matter 
of Thought, yet matter having characters as a product of 
Thought that may be recognized as of its own originating, 
and therefore legitimate and valid for its further uses. It 
becomes important, therefore, to determine precisely the 
allowed limits and conditions of such transformation, so that 
the new Judgment must be recognized as valid. It will be 
expedient to recall here some of the fundamental principles 
and characters of Thought as already ascertained and ex- 
pounded. 

All Thought, then, proceeds under the relation of Identity. 
It is valid only as the principle of the Same and the Differ- 
ent — the Identical and the Non-identical validates it. 

Moreover, as Thought is an activity continuing through 
time, as it moves on over the Same, the principle of repeti- 
tion necessarily comes in, and, under the form of Synthesis, 
or its opposite, Analysis, exerts its sway over the movements 
of Thought. All valid Thought, accordingly, is under the 
relations of Quantity — of Whole and Parts, so that where- 
soever these relations are given to Thought in any object or 
matter, Thought may move, and can move only when they 
are thus given. Quantity, in fact, is but identity identified 
— the result of repeated identifications. 

Further, the only essential relationships in Quantity are 
the two relationships : (1) of Whole to Part, with its recip- 
rocal of Part to Whole ; and, (2) of Part to Part. All 
Thought must, to be valid or legitimate, proceed in one of 
these two relationships, in their positive or their negative 
forms ; and all thought that is in these relations is so far 
valid - — in other words, bears the character of necessary 
truth. 



, 96 PURE LOGIC. 

All relations, other than these two relations of Quantity — 
those of Whole to Part, and of Part to Part — are foreign to 
Thought ; they are without its proper characters, the charac- 
ters of necessary truth, and are termed, in distinction, Prob- 
lematic, Contingent, Probable, Possible, according to the 
various degrees or kinds of modality. Hence the necessity 
of keeping in mind clearly the boundaries between the mere 
datum, or matter of Thought, and Thought itself. Only so 
far as we intelligently observe this distinction, can we accept 
any result in our thought as necessarily valid. 

Once more, the data, the objects of Thought, are greatly 
diversified. The applications of Thought, therefore, to attain 
the objects of our thinking, must accept these diversities in 
the essential qualities of its matter. It can do this, however, 
only within the limitations of its own proper sphere ; only, 
therefore, under the limitations of Quantity. It may, thus, 
assume the different kinds of Whole that are given to it, 
which, as we have seen, are the Integral, the Substantial, 
and the Causal ; and in order to any trustworthy results in 
the interest of truth, it must be able to discriminate these 
different kinds of Whole, and thus avoid confounding them 
in its movements. 

This recapitulation of the principles of Thought will guide 
us in the enumeration of the changes possible by thought in 
a given Judgment, that shall be legitimate changes, and so 
bear the characters of necessary truth. 

§ 60. The first kind of Immediate Reasonings is that of 

Conversion, in which the terms of the original 

Judgment, its Subject and Predicate, are simply 

transposed. Its formula is: A = JB; therefore, B=A. The 

primitive Judgment is called the Oonvertend ; the derived 

Judgment, the Converse* 

The validity of this Reasoning is too obvious to require 
extended proof or illustration. It has been already observed 
that it is not Thought itself, but the occasion or the design of 
Thought, which determines which of the two objects presented 



REASONINGS. 97 

to it shall be viewed as subject and which as predicate. 
Thought itself only identifies the two. It is, consequently, 
indifferent to Thought which of the two be the occasion or 
starting point. The conversion of a Judgment cannot, ac- 
cordingly, in any way affect its validity. 

The Law of Identity, which presides over every movement 
of Thought, here prescribes that there be no change in the 
quality of the Judgment, and none in the kind of Whole, that 
is, in the quantity of either term. The specification of the 
diverse applications of this Law in the conversion of a Judg- 
ment, with the indications of the necessity for a peculiarly 
careful attention to it in certain cases, will properly come 
under consideration in the Second Part of Logical science — 
the Doctrine of Methodology. 

§ 61. The second kind of Immediate Reasonings is that by 
Quantitative Restriction, in which one or both of Quantitative 
the terms, regarded as wholes, are changed to a Restriction. 
logical part or parts. Its formula is : A is B, therefore some 
A is B, The primitive Judgment is called the Restringend ; 
the derived Judgment, the Restricted, 

The logical validity of this form of Immediate Reasoning 
is equally obvious as that of the first kind by Conversion. 
Every whole is made up of like parts, each one of which 
may be recognized as identical, in some respect, with any 
other coordinate part. If the whole, therefore, is identified 
with another whole, any part may be identified with any like 
part of the second whole. 

If the Restriction is confined to but one of the terms, 
either the Subject or the Predicate, it is called Unilateral ; 
if extended to both terms, it is called Bilateral. 

Examples of Unilateral Restriction in Quantity are — 

1. Of Subject: Man is rational animal; therefore, Soc- 
rates is rational animal, 

2. Of Predicate : Man is rational animal; therefore, man 
is rational, 

■ 7 



98 PURE LOGIC. 

Of Bilateral: Man is rational animal; therefore, Socrates 
is rational. 

The Law that governs in this movement of Thought, is 
that of Identity as applied to the relation of Part to Whole. 
What is true of the Whole distributively is true of every 
part. 

§ 62. The third kind of Immediate Reasonings is that by 
Modal Re- Modal Restriction, in which the modal energy of 
striction. | ne Judgment is reduced; as, A must be B; 
therefore, A is B. 

Nothing need be said to illustrate the validity of this proc- 
ess of Thought. We have distinguished two kinds of Modi- 
fied Judgment, — the Necessary, where the ground of the 
Judgment is given as lying in the Thought itself; and the 
Problematic, where the ground of the Judgment lies out of 
the proper sphere of Thought. The other kind of Judgment 
given by this distinction is, of course, the unmodified, or the 
simple Assertory. Now it is plain that the Necessary must 
always involve both the Problematic and the Assertory, in- 
asmuch as if Thought has once identified, its identification 
being absolute and sovereign throughout the realms of 
Thought, the terms it has once identified in a necessary 
Judgment are ever and everywhere, whether simply or 
problematically, identified ; as, 3 -j- 1 = 4* being a necessary 
Judgment, these terms may with absolute validity be ac- 
cepted as identical in any matter foreign to Thought — any 
contingent matter. 

The governing Law in this process of Thought is, as in 
the last enumerated, that of Identity as applied to the rela- 
tion of Part to Whole. Here the whole is one of Degree or 
Intensity, as it lies in the judging act, not in the matter 
judged. The stronger ever includes the weaker. 

§ 63. The fourth kind of Immediate Reasonings is by 
Transfer- Transference, in which some character of the 
ence. Thought in the copula is transferred to the mat- 

ter in the terms ; as, A is not B ; therefore, A is non-B. 



REASONINGS. 99 

This process of Thought, although generally recognized by 
logicians as of unquestioned validity, evidently lacks the 
character of perfectly pure Thought. It is not necessarily 
valid, because it accepts the intermingling of Thought with its 
matter as legitimate, whereas to confound the qualities of the 
thought with those of its matter is precisely the grand source 
of error against which the Science of Logic chiefly seeks to 
guard. That such a transference is not of itself legitimate 
will be apparent from a single example. Substitute in the 
formula given, for A, a stone, and for B, vertebrate ; we shall 
then have the reasoning : A stone is not vertebrate ; therefore, 
it is non-vertebrate ; that is, invertebrate. It is obvious that, 
in the transference, we have changed the Thought from being 
purely negative in its quality to one having something of a 
positive character. Our conclusion is a palpable falsity, as 
we have ranked a stone among the class of invertebrates. 
We must not at once conclude that this process is wholly 
extra-logical. It is assuredly a process of Thought ; and 
nothing that concerns Thought can be regarded as extra- 
logical. It is the part of logic to separate the element of 
pure Thought from the hybrid process, and so indicate pre- 
cisely what there is of logical validity in it. Certainly there 
is a semblance of legitimacy in the process, else logicians 
would not so universally have accepted it wifohout question, 
for we find it thus accepted by logical purists of the first 
degree, who have insisted upon exterminating from the science 
every weed of matter, and upon keeping the field entirely 
free to the purest forms of Thought. It will not be difficult 
to discriminate the matter from the form here, and thus to 
attain the proper criteria for the validity of such a process 
in our thinking. 

We have found the relations of Whole and Parts to be the 
proper relations of Thought. Any procedure under these de- 
lations is a legitimate and valid procedure of pure Thought. 
If, consequently, any matter given to Thought be given in 
these relations, then Thought can move on in necessary cer- 



100 PURE LOGIC. 

tainty as pure Thought. So far, then, as the transfer of a 
quality of the copula from it to either of the terms is within 
this relation of Whole and Part, it is valid. Thus, substitut- 
ing for B, in the example given, a term thought as a Whole, 
of which vertebrate and invertebrate are logically Complement- 
ary Parts, and for A, a term given as a part of that Whole, 
say butterfly, then the transference of the negative becomes 
valid — we can conclude, Butterfly is invertebrate. We have 
now avoided the intermingling of thought and matter ; the 
movement has been within the proper sphere of Thought ; 
from the proper field of a Judgment, in fact, to that of a Con- 
cept. The obvious limitation on this mode of reasoning, thus, 
is that the first form (B) of the term to which the quality of 
the Judgment is transferred be recognized as a part comple- 
mentary of the second form (non-B), and that the other term 
(A) be recognized as lesser part of one or the other of these 
complementary parts. 

The logical validity of the Thought as thus regulated is 
obvious on the principle that in a given whole any one part 
is complementary of the rest, and reciprocally the rest is 
complementary of it ; and that any lower part of that whole 
must belong to one of these complementary parts. If, thus, 
there be a whole C, of which A and B are parts, and B and 
non-B are the two complements of that whole, if A is not B, 
it necessarily is non-B. Otherwise ; A being some part of 
(7, and B and non-B being also complementary parts of (7, 
if A is not B, it must be non-B. 

This form of Immediate Reasoning, by transference of 
Quality from the copula to one of the terms, is legitimate 
in each species of Wholes. Thus, in a Spacial Whole, if by 
A and B in the formula given be understood respectively 
halves of a square bisected by a diagonal, we shall have : 
This half — A — is not B; therefore, it is non-B. 

So in a Substantial Whole ; if rational and animal be 
parts, making up the same whole, man ; then if (A) animal 
is not (B) rational, it is (non-B) non-rational ; or (A) an- 



REASONINGS. 101 

imal is not (B) rational; therefore, (A) animal is (non- 
B) non-rational, that is, irrational. 

In the same way, in a Causal Whole, if a magnet be viewed 
as a cause acting, the parts through which are attraction and 
repulsion complementary of each other, so that magnet in 
this use of the term, as a cause only, attracts or repels, then 
we may reason: if this acting magnet does not attract, then 
it does non-attract, that is, repel ; — non-attracting being here 
repelling, or the necessary alternative, that is, the comple- 
mentary part of attracting in an acting magnet. 

Reasonings by Transference are of two varieties. 1. The 
proper Quality of the copula may be transferred Transfer- 
to one of the terms ; as, Mind is not material ; Qualitative • 
therefore, it is immaterial ; Necessity does not be- 2 - ModaL 
long to rational being ; therefore, non-necessity, that is, Free- 
dom, belongs to rational being. 

2. The Modality of the copula may be transferred to one 
of the terms ; as, Rain may fall to-morrow ; therefor e,Rain is 
a possible event to-morrow. 

The exposition given so far of this form of Immediate 
Reasoning has, for the sake of clearness, proceeded in forms 
of illustration appropriate strictly and throughout only to the 
first of these varieties. The movement of Thought we found 
to be valid, inasmuch as Thought did not move out of its own 
sphere — kept within its own proper relationships of Whole 
and Part, or more specifically within relations of Contradict- 
ory Disjunction. It is equally valid in the second variety, 
if only a proper modality of Thought be transferred. If the 
derived Judgment be interpreted as under a modality of 
Thought, the reasoning is obviously not universally, that is, ne- 
cessarily, valid. Thus, in regions where rain is only in one 
part of the year, although a stranger ignorant of the pecul- 
iarities of the climate might reason with himself, so far as 
thought can go : Rain may fall to-morrow ; therefore, Rain 
is a possible event to-morrow, it would be a false conclusion, 
if the modal word possible were to be interpreted as expres- 



102 PURE LOGIC. 

sive of physical modality. Only so far as proper modality of 
thought, can modality, thus, be transferred from the copula to 
the terms — from the thought to the matter. 

In order to effect the transference legitimately, it may be 
necessary to bring into the antecedent another Judgment, so 
that we shall have a Mediate Reasoning. Thus, in the first 
case, we may need to add for a logical antecedent to the 
Judgment, A is not B, the Judgment, A is part of B, or of 
non-B. Then the conclusion is legitimated. 

§ 64. The fifth kind of Immediate Reasoning is that of 
Disjunction. From a Disjunctive Judgment we 
lsjuncion. ma ^ immediately infer both, (1.) That the dis- 
junct members are not the same ; and, (2.) That the one is 
contradictory of the other. Thus from A is either B or 0, 
we may immediately infer either, (1.) That B is not C ; or, 
(2.) That non~B is C. Or Angles are right, acute, or obtuse ; 
therefore, (1.) Right angles are neither acute nor obtuse ; 
and, (2.) No acute angle is either right or obtuse. 

The validity of this reasoning is evident from the nature 
of Disjunction, which is the principle of the relation of Part 
and Complementary Part. 

§ 65. The sixth kind of Immediate Reasoning is that of 
Composition, in which, from several Judgments 

Composition. x . 7 . ° 

with the same term either as subject or predicate, 
a Judgment may be derived in which, with this term remain- 
ing, the other term shall be the sum of the other terms. 
Thus, if A is B, and G is B, then A-\-C is B ; or, If animals 
are organic and vegetables are organic, then animals and 
vegetables, that is, all living beings, are organic. If all body 
has length, and all body has breadth, and all body has depth ; 
then all body has length, breadth, and depth, that is, is solid. 

The principle of this kind of Immediate Reasoning is ob- 
viously that of the Concept. No further illustration of its 
nature or validity is necessary. 

§ 66. Mediate Reasonings we have distinguished into two 
Categorical c l asses > according as they embrace or not new 
Syllogism. matter not in the primitive Judgment. Those of 



REASONINGS. 103 

the first class in which new matter is introduced, if the new 
matter be in a single term of a single new Judgment, are 
called Categorical Syllogisms, We thus have the following 
definition : — 

A Single Categorical Syllogism is one whose ante- 
cedent member contains two Judgments, to which Itg3 ) efin i. 
but one term in each is common, the other being tion - 
different ; as, Man is mortal ; Caius is a man ; therefore, 
Caius is mortal. 

In this example, the first Judgment in the antecedent 
member of the Reasoning contains for its matter the terms 
man and mortal ; the second Judgment contains, besides the 
term man in the first, new matter in the term Gains. 

The nature of this movement of Thought it will not be 
difficult to render intelligible. A primitive condition of 
Thought we have found to be a Law imposing upon it, if it 
move at all, the necessity of recognizing the identity or the 
non-identity of any two objects presented to it. Now as the 
essential quality of Intelligence is clearness, it may be im- 
possible for Thought to move at all, to recognize identity or 
non -identity, that is, affirm sameness or difference, for want 
of light. It necessarily, therefore, remains in doubt. A new 
cognition in the form of another Judgment may afford the 
requisite light, and enable the Thought to move from the 
state of doubt to that of a determinate Judgment. 

This new enlightening Judgment, however, must stand in 
a certain definite relation to the two terms that were origin- 
ally presented to be identified or differenced ; and this rela- 
tion must be one that lies within the sphere of Thought ; — 
must be, in other words, a relation of Quantity — of Whole 
to Part, or of Part to Part. If the two original terms, say 
A and G, were, one of them, A, a whole of which another 
term B were a part, and B also were a whole of which G 
were a part, then Thought could at once move in its own 
sphere of Quantity and recognize (7, inasmuch as it is a part 
of B, as also a part of A of which B is a part ; in other words 



104 PURE LOGIC. 

conclude that, if C is a part of B, and B is a part of A, is 
a part of A. This may perhaps be better illustrated in a 
concrete example. . We may have the two objects of thought 
given to us, of sponge and animal ; and may be unable for 
want of light to recognize any identity between them so as to 
be warranted in affirming that the sponge is an animal, or in 
affirming that a sponge is not an animal — we stand in doubt. 
But by the aid of new Judgments, as that the sponge is sen- 
tient, and that all sentient beings are animal, this doubt is re- 
moved, as we recognize that, the sponge being a part of 
sentient beings and sentient beings a part of animal, the 
sponge must be part also of animal — that sponge is identical 
with part of animal. 

This illustration characterizes but one of the two great 
classes of Mediate Reasonings — the so-called Deductive 
Reasonings or Syllogisms. Logicians have generally limited 
their view to this species, giving but incidental consideration 
to the other. Indeed, many, like Dr. Whately, have endeav- 
ored to subordinate all forms of Reasoning to the Deductive 
Syllogism, and with him the terms Reasoning and Syllogism 
are convertible. Sir William Hamilton has exposed the 
error of those views, but has failed to elaborate any trust- 
worthy scheme that should comprehend all reasoning. In- 
deed, he seems to have utterly overlooked one of the two fun- 
damental relationships in Thought. While recognizing all 
Thought as necessarily proceeding in the relations of Quan- 
tity, he has seemed to regard but one specific relation among 
them, viz : that between the Whole and Part ; or, more exactly, 
perhaps, he makes of this single relation two — that from the 
Whole to the Part, and the converse, from the Part to the 
Whole, forgetting that these two supposed relations are 
necessarily one in Thought, the movement being indifferent 
so far as Thought is concerned, in the one direction or in the 
other, and that it is the object or proposed aim in thinking, 
the occasion external to the thought, that determines the 
direction of the movement, whether from this goal or from 



SEASONINGS. 105 

that, from the Whole or from the Part. The relationship 
between the Whole and the Part, thus, is the same, whether 
we think that the Whole contains the Part, or that the Part 
is contained in the Whole ; and the distinction of Hamilton is 
fallacious or utterly futile. But there is another entirely dis- 
tinguishable relation of Quantity — that of Part to Part. 
Only as we admit this relation between part and complement- 
ary part in every whole, can we admit any disjunction in 
Thought — any recognition of Same and Different. The very 
notion of Difference implies a necessary relationship between 
Parts. This relation between Part and Complementary part, 
given at once and necessarily with the relation of Whole and 
Part, permeates Thought everywhere as its validating con- 
dition. 

§ 67. Categorical Syllogisms are divided into two classes 
in respect of the two different directions in which Thought 
may move. If the movement be between the two relatives 
of Quantity, Whole and Part, the Syllogism is called De- 
ductive. If, on the other hand, the movement of Thought 
be between relative Part and Part, the Syllogism is called 
Inductive. A Syllogism of either class may alike proceed 
either in Comprehensive or in Extensive Quantity. 

§ 68. A Deductive Syllogism is a Mediate Reasoning 
in which the movement of Thought is from a Whole to a 
Part, mediated through a middle term, which is, respectively, 
a part of that whole and a whole of that part ; as, Man is 
mortal ; Caius is a man ; therefore^ Caius is mortal. 

As the Deductive Syllogism is a Mediate Reasoning, its 
datum must consist of two Judgments, which, as given to 
Thought, are not of course at all validated by the Reasoning. 
They must be regarded consequently as only assumed for 
the Reasoning, or must rest on evidence foreign to it. But 
the movement of Thought in itself may be valid, although 
the given Judgments are false ; just as an arithmetical proc- 
ess may be correct, although applied to unreal objects. 

These two given Judgments constitute the Antecedent ; as 



106 PURE LOGIC. 

the derived Judgment is the Consequent of the Reasoning. 
From their naturally preceding the Consequent, they are 
called the Premises (Propositiones prcemissce). 

As might be supposed, not any two Judgments taken for- 
tuitously can be accepted as premises in the same Reasoning. 
In the first place, both of the Judgments must contain the 
same term in common, the other term in each being different. 
In the next place, this term that is common to the two Judg- 
ments, must be a part in relation to the remaining term in 
one Judgment, and, also, a whole in relation to the remain- 
ing term in the other Judgment. Thus, in the example 
given, the term man is a part of the class mortal, but a whole 
class of which Oaius is part. From its bearing this two- 
fold relation to the remaining terms in the premises, of part 
to one, and of whole to the other, this common term is called 
the Middle Term ; and the other terms are called the Ex- 
tremes (extrema^ axpa). When this relation exists, and only 
then, can two judgments be accepted as premises ; and, to 
use the expression of Aristotle, " when the three terms are 
so related to one another that the last is in the middle as a 
whole, and the middle is or is not in the first as a whole, a 
perfect syllogism necessarily emerges." 

Of the Extremes, that which as a whole contains the 
Middle Term is called the Major Term ; and that which is 
contained in or under the Middle, is called the Minor Term. 

A convenient mode of designating the Terms is by the use 
of the letters W, P, and M : W denoting the Major Term ; 
P, the Minor; and M, the Middle. 

The very nature of the process excludes the possibility of 
there being more than these three terms in a single Deduc- 
tive Reasoning — the two Extremes being compared through 
the Middle Term. A Term, it must be recollected, may con- 
sist of several words ; they must, however, constitute one 
object of thought, and so be capable of being used as a sub- 
ject or as a predicate. On the other hand, if a single word be 
used in different meanings in the several propositions which 



REASONINGS. 107 

compose the Syllogism, we have, under the guise of three, 
in reality more than three, terms. This is the nature of the 
fallacy of four terms, quaternio terminorum. As in the Syl- 
logism : 

Animals are void of reason ; 

Man is an animal ; 

Therefore, man is void of reason. 

Here the middle term, animal, is used in the Major pre- 
mise as synonymous with brute, a conspecies of man, and so 
excluding it. In the Minor premise it is used to denote a 
genus containing under it the two species, rational and irra- 
tional ; — as, in other words, including man. There are, 
thus, really two different objects of thought, two logical terms 
presented in the tw T o premises by the same word — animal. 

In respect of the Propositions, it is equally clear that there 
must be one showing the relation between the Major term and 
the Middle term — - a proper Sumption ; that there must be 
another showing the relation between the Middle and the 
Minor — a proper Subsumption ; and, moreover, a Conclu- 
sion, showing the relation between the Major and the Minor. 

The Hindoo system seems to have recognized five propo- 
sitions, called the Assertion, the Reason, the Proposition, the 
Assumption, and the Deduction in a Reasoning : as " 1. The 
mountain has fire ; 2. For it has smoke ; 3. But all that has 
smoke has fire ; 4. And the mountain has smoke ; 5. There- 
fore, the mountain has fire." But it is apparent that the first 
proposition, which is called the Assertion, is the same as the 
fifth, the Deduction or Conclusion ; and the second, called the 
Reason, is the same as the fourth^ called the Assumption. 
There are, in fact, only three propositions entering into the 
Reasoning proper. The premises must be regarded for the 
Reasoning as assumed ; they are the data to Thought in its 
movement. 

Of the two premises, that one which enounces the relation 
of the Major term to the Middle, is called the Major Pre- 
mise, also the Sumption (propositio major, sumptio major, 



108 PURE LOGIC. 

sumptio, thesis). The other of the premises which enounces 
the relation of the Minor Term to the Middle, is called the 
Minor Premise, also the Subsumption (propositio minor, as- 
sumptio, subsumptum, subsumptio, sumptio minor). It is not, 
of course, the order in which the premises are placed in the 
Syllogism which determines the one to be the Major, the 
other to be the Minor Premise. The order is merely of the 
form, the verbal expression, and does not concern the thought. 
Which shall precede is, hence, a matter of indifference so 
far as the essential character of the reasoning is concerned. 

The Consequent is the derived Judgment — the result or 
goal of the Reasoning. It enounces the relation of the Minor 
term to the Major, and is called the Conclusion {conclusio, 
collection o-vfJL7r€pao'}Aa). It is usually, in formal and fully 
stated Syllogisms, designated by the Conjunction, therefore, 
or by synonymous expressions, as consequently, and the like. 

Logicians, recognizing only Extensive Quantity, and having 
accepted the division of Propositions into the four kinds, Uni- 
versal Affirmative, Particular Affirmative, Universal Nega- 
tive, and Particular Negative, as their ruling division, have 
connected the consideration of Quantity with that of Quality 
in their formal treatment of the Syllogism. It has been, 
accordingly, prescribed by them that the Sumption must be 
definite, that is, universal or single, while the Subsumption 
may be in either Quantity, definite or indefinite. But this 
teaching is all unnecessary, and tends to confuse and to mis- 
lead. The one principle is that each term must in each sev- 
eral proposition be taken in the same meaning in respect of 
Quantity, as well as in respect of nature of object denoted by 
it. If the Minor term be restricted by any limiting word, as 
some, few, or the like, while it is yet recognized in the Syllo- 
gism as being contained unrestricted in the Middle, we have, 
in fact, a mixed reasoning — a proper mediate reasoning com- 
bined with an immediate reasoning of the Restrictive Class. 
It is clear we cannot reason : Some men are learned; Oaius 
is a man ; therefore, Gaius is learned, simply because the 



REASONINGS. 109 

Middle term in the Sumption is not used in the same extent 
of meaning as in the Subsumption. There are really four 
terms. When we have a Subsumption in Particular Quan- 
tity, so-called, as, for example, Man is mortal ; some rational 
beings are men ; obviously we cannot conclude : therefore, 
rational beings are mortal ; for we have changed the mean- 
ing of the Minor term, using it in a wider extent in the Con- 
clusion, and a narrower in the Subsumption. But commonly, 
if the Minor term be used in a wider extent of meaning in 
the Subsumption than in the Conclusion, as, Man is mortal ; 
philosophers are men ; therefore, some philosophers are mortal, 
we have a valid conclusion, it is true, but a mixed reasoning, 
as just stated. 

Logicians have enounced the comprehensive rule for the 
conclusion, thus : The Conclusion must always follow the 
weaker or worser part, the negative and the particular being 
regarded as the weaker or the worser in respect of the affirm- 
ative and the universal. 

The general relations of the several judgments which com- 
pose a Deductive Reasoning to one another, moreover, logi- 
cians have illustrated to the eye by means of three unequal 
circles, the largest of which represents the Major term, the 
smallest the Minor, and the intermediate the Middle term. 
If we call them respectively W, P, and M, then it will 
readily be seen if the largest circle, W, include the middle 
circle, M, and if, also, M include the least circle, P, the 
largest circle, W, must include the least circle, P. 

§ 69. As the relation of Whole and Part may exist in 
either of the two kinds of Logical Quantity, Ex- 

~ '...,. J Two kinds 

tension or Comprehension, it is obvious we may of Deductive 
have two kinds of Deductive Syllogism, the Ex- y ° glsm * 
tensive and the Comprehensive or Intensive. 

In the Extensive form, the Middle is said to be contained 
under the Major term, and to contain under it the 1 Extensive 
Minor term. In the Intensive form, the Middle is 2 - intensive. 
said to be contained in the Major term, and to contain in it 



110 PURE LOGIC. 

the Minor term. The Syllogism, as ordinarily expressed, 
may be explicated in either Quantity. Thus in the Syllogism, 
Man is mortal; Caius is a man ; therefore, Oaius is mortal, 
if we explicate it as in Extensive Quantity, we shall have the 
following : 

The Middle term, man, is contained under the Major term, 
mortal ; that is, man is a part of the class mortal: 

The Minor term, Caius, is contained under the Middle 
term, man ; that is, Cains is a part of the class man : 

Therefore, the Minor term, Caius, is contained under the 
Major term, mortal ; that is, Caius is a part of the class mortal. 

If, again, the Syllogism be construed as in Intensive Quan- 
tity, the explication will be as follows : 

The Major term, Caius, contains in it the Middle Term,, 
man ; that is, the complement of attributes, Caius, contains 
in it, as part, the complement of attributes, man : 

The Middle term, man, contains in it the Minor term, 
mortal ; that is, the attribute, man, contains in it, as part, the 
attribute mortal : 

Therefore, the Major term, Caius, contains in it the Minor 
term, mortal; that is, the complement of attributes, Caius, 
contains in it as part the attribute mortal. 

It will be noticed that the term man is the Middle term in 
each explication ; but the two other terms change places ; — 
the Major term in the Extensive form becoming the Minor 
in the Intensive ; and the Minor in the former becoming the 
Major in the latter. Accordingly, the Major premise, which 
in the Extensive form compares the Major term, mortal, with 
the Middle term, man, in the Intensive form compares Caius, 
as the Major term, with the Middle ; and a corresponding 
change takes place in the Minor premise. In other words, 
the Premises change with the changed relations of the Ex- 
tremes to the Middle term. 

It will also be seen that the one may easily be converted 
into the other without affecting the validity of the reasoning. 
But the formula W contains M ; M contains P ; therefore, 



REASONINGS. Ill 

W contains P, is the one universal formula for all Affirma- 
tive Categorical Syllogisms in either quantity. This, how- 
ever, may be stated in the passive form, but then preposi- 
tions come into use, and the kind of quantity is at once indi- 
cated by them. Thus, in Extensive Quantity, it would be 
expressed : M is contained under W ; P is contained under 
M ; therefore^ P is contained under W. While, in Intensive 
Quantity, we should have : Mis contained in W ; P is con- 
tained in M; therefore, P is contained in W. 

In Extensive Quantity, it will be recollected, a term always 
denotes a class or a part of a class ; while in Intensive Quan- 
tity it denotes an attribute or a complement of attributes. 
And the formula of the Categorical Deductive Syllogism 
would be explicated in Extensive Quantity thus : 

1. Affirmative : The class W contains under it the class 
M ; the class M contains under it the class or individual P ; 
therefore, the class W contains under it the class or individ- 
ual P. 

2. Negative : The class W does not contain under it, en- 
tirely excludes, the class M ; the class M contains under it 
the class or individual P ; therefore, the class W does not 
contain under it the class or individual P. 

In Intensive Quantity it would be explicated thus : 

1. Affirmative: The attribute W contains in it as part 
the attribute M ; the attribute M contains in it as part the 
attribute P ; therefore, the attribute W contains in it as 
part the attribute P. 

2. Negative : The attribute W contains in it the attribute 
M ; the attribute M does not contain in it, entirely excludes, 
the attribute P ; therefore, the attribute W does not contain 
the attribute P. 

While the entire reasoning as expressed in the ordinary 
forms of discourse may be explicated in either quantity, it 
would plainly be incorrect to explicate a part of it in one 
quantity and the rest in the other quantity ; — to explicate, 
for instance, one premise in Extensive Quantity, and the 
other premise or the conclusion in Intensive Quantity. 



112 PURE LOGIC. 

§ 70. An Inductive Syllogism is a Mediate Reason- 
induction * n S> * n wn i ca the movement of Thought is from a 
defined. given part to its complementary part ; as, Affir- 

mation is Thought ; but negation is the complementary of affir- 
mation ; therefore, negation is Thought : P is W ; C is com- 
plementary of P ; therefore, C is W. 

We have found two general relationships in Thought as a 
relative cognition, each equally primitive and ne- 

Explication. .. ,. -, ,. . . 

cessary, coordinate, and, moreover, conditioning 
each the other. They stand, indeed, in this respect, precisely 
on the footing of the two Laws of Identity and Contradic- 
tion in their relations to the two Law T s of Disjunction and 
Exclusion. The one relationship is that of Whole to Part ; 
the other is that of Part to Part. That there is a part, in- 
volves the necessity of there being another part or parts, 
which one part or which several parts are the complement 
of the first. We have, then, standing side by side with the 
principle that the whole contains its parts, the coordinate 
principle that a part necessitates in Thought its complement- 
ary part. 

Now this complementary part is, in some respects, identi- 
cal with the other part ; in other respects it is different from 
it. Just so far as they are parts of the same whole they are 
identical ; but so far as they are complementary of each other 
they are different. If two triangles are parts of the same 
square bisected through its opposite angles, they are identi- 
cal in respect of length of sides, angles, surface ; they are 
different in being complementary parts, the one lying in one 
direction from the bisecting line, the other in the opposite 
direction from that line ; in short, they are as complementary 
to each other, related as positive or affirmative and nega- 
tive in reference to the principle of bisection. What is thus 
evident in an Integrate Whole, is equally true in the Whole 
of Substance. If rational arid animal are the component 
parts of man, then so far as they are parts of the same 
whole, they are identical ; that is, if as a part of man, as 



REASONINGS. 113 

living substance, rational is living, we necessarily infer that 
animal, as such part, is also living. As complementary of 
each other they are different ; animal is the irrational part 
of man. In like manner, in a Causal Whole, if ashes and 
smoke are complementary parts of the effect of combustion 
conceived as a whole, then, in some respects — for instance, as 
products of combustion — they are identical; in other re- 
spects, as complementary, they are different ; one is the solid, 
the other is the non-solid — the gaseous product of com- 
bustion. In a logical Whole of Extension, the two species 
which in the strict dichotomous division make up its parts, 
are of course complementary of each other. They are iden- 
tical in so far as they participate in the whole ; they are dif- 
ferent in so far as they are conspecies. Interpreting animal 
thus in Extensive Quantity, that is, as denoting a class, we 
have, as two species contained under it, rational animals 
and irrational animals, that is, men and brutes. Now what- 
ever is true of men so far as animal, is true of brutes so far 
as animal. This follows, indeed, necessarily, from the very 
nature of a Concept. On the other hand, in so far as they are 
conspecies, and accordingly complementary of each other, 
they are different. In so far as man is rational, man is differ- 
ent from brute. And it is plain that whatever part of what 
is merely animal is in man must belong to whatever like part 
is animal in brute ; while whatever part of rational is found 
in man differs from whatever like part pertains to brute. 
And here, in strictly logical or dichotomous division, difference 
is contradiction ; so that we may infer that if man has a 
digestive system necessarily as animal, brute has, as animal, 
a like system ; and on the contrary, if as rational man is 
free, brute as irrational is not free. The same view holds 
good of Intensive Quantity so obviously as to require no 
distinct consideration. The validity of this kind of thought 
here discovers its ready and certain test. If our Concepts 
in which we reason are valid, our Induction is so likewise. 
Such is the simple nature of all Induction as a process of 
8 



114 PURE LOGIC. 

Thought. It is a clearly distinguishable process from De- 
duction, and is precisely coordinate with that process — its 
exact complement as a derivation of a Judgment. It gives 
the character of absolute, apodictic certainty to its result. 
Extremely simple as it is, it imparts all there is of certainty 
or of probability to that infinite diversity of inferences in 
scientific investigations, in art-contrivances, in common life, 
which we call by this name of Induction — a far wider move- 
ment of thought, as already observed, and far more impor- 
tant, every way, than its coordinate, Deduction. It is to 
that, what Addition is to Subtraction in Arithmetic ; and the 
two, Induction and Deduction, are to all our multifarious 
thinking what Addition and Subtraction are to all the possi- 
ble and complicated operations in the limitless sphere of nu- 
merical calculation. And as no such calculation has any 
validity except on the principle that one added to one equals 
two, so all our induction in its multifarious forms is valid only 
on the principle that a part necessitates its complement We 
discover, here, moreover, an exact analogy to the logical proc- 
ess of Disjunction. While Logic strictly validates only 
Contradictory Opposition in Disjunction, as of absolute ne- 
cessary certainty, yet it shows how Contrary Disjunction may 
fee validated by reduction to Contradictory, and thus enables 
us to secure the character of truth to those concise and com- 
plicated movements in which Thought in common life gener- 
ally proceeds, just as Multiplication is a concise complicated 
process of Addition. So in Induction, while Logic strictly 
accepts only the immediate relationship in thought of Part 
and its Complementary Part, it yet shows how far this move- 
ment may be validated in the relationship of any Part to 
any other of manifold Parts in the same Whole. 

As in Deduction, in precise logical strictness, we can rea- 
son only step by step down the gradations of parts, in 
regular succession, and must always be able, in order to val- 
idate our reasoning, to indicate each gradation, but yet may 
reason to a remote part of a part — may leap down over 



SEASONINGS. 115 

many steps in a single movement of Thought : so in Induc- 
tion, extremest logical rigor requires us to reason only to one 
complementary part ; yet it allows us, while maintaining our 
ability to verify our procedure by a reference to this its 
single ultimate principle, to reason to remote gradations of 
complementary parts. Thus, as in Deduction, if rational be 
part of concept man ; and intelligent, part of rational ; and 
discriminative, part of intelligent ; and comparative, part of 
discriminative, we may safely conclude that man is compara- 
tive, through any middle — rational, intelligent, discriminative 
— although to verify our procedure we must go through each 
successive gradation ; so in Induction, if rational be comple- 
ment of animal ; and intelligent, as part of rational, be com- 
plement of moral ; and discriminative, as part of intelligent, 
be complement of intuitive ; then we may infer by induction 
that if animal is living, then the remote complement of a 
remote part of rational, which we have assumed to be the 
complement of animal, is also living. The principle is the 
same as in the process when limited to the first gradation, 
and validates as of absolute certainty the abbreviated pro- 
cess. Indeed, we have here, as it has been indicated to be 
with Multiplication in respect to Addition, only a compen- 
dious method of thought, which we can test and validate only 
by a full exposition of the process into the full and formal 
statements of the Syllogism. 

All Induction, thus, is in its essential nature a Mediate 
Reasoning, in which the agreement or difference between two 
objects of thought is recognized through their respective rela- 
tion to a third. While in Deduction the thought moves from 
Whole to Part, in Induction it moves from Part to Part. In 
strictest logical accuracy these two parts are exactly and 
fully complementary of each other, making up one whole of 
thought. But as we may have valid thought proceeding in 
contrary opposition as well as in contradictory which is the 
strictly logical opposition, so we may have valid thought in the 
relations of any part of one of these two primitive complement- 



116 PURE LOGIC. 

aries to any like part of the other. Indeed, as most of our 
thinking is in fact in contrary rather than in contradictory 
opposition, so likewise most of our thinking is in fact in the 
relationship between the lower gradations of parts. And as 
we validate thought in contrary opposition by reducing it to 
contradictory, so likewise we validate reasoning in the rela- 
tions of the lower gradations of parts by reducing it to those 
between the two primitive complementaries. 

Under the Postulate that has been enounced, § 18, all 
valid Induction may be expressed in the formal Inductive 
Syllogism. This, like the Deductive, contains three Prop- 
ositions which have as their subjects and predicates three 
and only three terms. 

Of these three Terms, two are parts that are complement- 
ary of each other; and one of these two is the mediating 
term of the reasoning, and may, hence, properly be called 
the Middle Term. The other two are the Extremes, that 
which denotes the whole being the Major Term, and that 
which denotes the part being the Minor Term. The terms 
may conveniently be indicated by the letters W, P, and C ; 
of which W denotes the major term, P the minor, and C the 
middle term. 

Of the three Propositions, two are given. They express 
the data to the thought in the Reasoning. They constitute 
the antecedent of the syllogism, and are called the Premises. 
The other expresses the derived judgment in the Reasoning^ 
or the Consequent. It is called the Conclusion. 

Of the two Premises, one expresses the relation between 
the middle term and that one of the extremes which ex- 
presses the whole. It may be called the Major Premise, or, 
better perhaps, the Sumption. The other premise expresses 
the relation between the middle term and the other extreme 
as its complementary. It may be called the Minor Premise, 
or the Subsumption. 

The Conclusion expresses the relation between the ex- 
tremes. It is signalized by the illative conjunction therefore, 
and its synonyms. 



REASONINGS. 117 

The formula of the Inductive Syllogism will thus be : 
S u m p tion : G is W ; 

Subsumption : P is complementary of G ; 
Conclusion : Therefore, P is W. 

Exemplifications in concrete matter, and in the two kinds 
of Quality, Affirmative and Negative, may be given thus : 

I. Affirmative Inductive Syllogism. 

Sumption: The Inferior Planets (0) shine by reflected 
light (W); _ 

Subsumption : The Superior Planets (P) are complement' 
ary of the Inferior Planets ( G) ; 

Conclusion : Therefore, the Superior Planets (P) shine by 
reflected light (W). 

This syllogism may be thus explicated : — 

Sumption : The middle term (C) Inferior Planets is part 
of the major term (W), the whole class of things shining by 
reflected light ; 

Subsumption: The minor term (P) Superior Planets is 
complementary of the middle term (C) Inferior Planets ; . 

Conclusion: Therefore, the minor term (P) Superior 
Planets is part of the major term (W), the whole class of 
things shining by reflected light. 

II. Negative Inductive Syllogism. 
Sumption : Venus does not revolve about the earth ; 
Subsumption : Uranus is a planet like Venus ; 
Conclusion : Therefore, Uranus does not revolve about the 

earth. 

The exposition which has thus far been given of the In- 
ductive Syllogism has, for the sake of clearness and simplic- 
ity, recognized it as proceeding only in Extensive Quantity. 
But it is equally valid in Intensive Quantity ; and the 
change is exactly correspondent to that already indicated in 
the Deductive Syllogism. 

We have accordingly the two kinds of Inductive Reason- 
ing distingished in respect of the logical quantity of the 
terms : The Extensive Inductive Syllogism, and the Inten- 
sive Deductive Syllogism. 



118 PURE LOGIC. 

It will not be necessary to give examples of the Intensive 
form ; for those already given may be easily explicated in 
this kind of quantity. 

From the fact that European logicians, perhaps by reason 
of the omission of Aristotle, the father of European logic, 
to elaborate any system of Inductive as he did of Deductive 
Reasoning, have recognized only Deductive in their exposi- 
tions and illustrations, the formal characters of the Inductive 
Reasoning are not so familiar to our minds as those of the 
Deductive. Indeed, but for the disproportionate elaboration 
of Deduction during the rise and early progress of European 
literature, shaping and coloring all its forms of expression, 
the full form of the Deductive Syllogism would undoubtedly 
be as strange to us as that of the Inductive ; for our ordinary 
thought does not flow in full logical forms — one of the prem- 
ises being generally omitted in reasoning. In Inductive rea- 
soning, the Subsumption is hardly ever expressed. It is the 
proper function of Logical Science to supply what is thus 
implied, thereby to validate the Thought. 

Induction, moreover, is used rather in the investigation of 
truth than in probation, which is more closely allied to De- 
duction. Its nature and validity will accordingly be more 
particularly illustrated under Methodology. See also Ap- 
pendix. 

§ 71. The second class of Mediate Reasonings we have in 
Conditional general terms distinguished from the first or Cate- 

Syllogisms: ° ' • . . _ . . .. . . . . . . 

— what. goncal class, by this peculiarity, viz : that in this 
second class the derivation of the new Judgment is effected 
through a Judgment as such — through the copula ; while 
in the first class, the derivation is through Concepts as such, 
in the channel of their reciprocal relations as Wholes and 
Parts. The Categorical Deductive Syllogism thus derives 
the new Judgment through the relation of its terms as re- 
spectively whole and part in respect to another term called by 
virtue of this twofold relation, middle, and the Categorical 
Inductive Syllogism derives the new Judgment through the 



REASONINGS. 119 

relations of its terms as respectively the whole and the 
complementary of another term which is called by virtue of 
this relation middle. In the Categorical Syllogism, thus, the 
reasoning is mediated through a term — a Concept. But, as 
we might anticipate as altogether a probable result, the medi- 
ation of the new Judgment may be effected through the 
proper essence of the Judgment ; so that instead of a Con- 
cept, a Judgment may form the proper middle of a reasoning ; 
and two Judgments, in so far as Judgments, and out of all 
regard to the relations of their terms, may stand in such 
relations to each other, that Thought, under its own proper 
law of Identity in its diverse phases, may legitimately move 
to a new Judgment. Such is the case in that class of Rea- 
sonings called Conditional. The name, it may be observed, 
is inadequate. It points only to one species of this class of 
Reasonings, called in the Greek, Hypothetical, a word ren- 
dered in Latin, Conditional. If, however, it be borne in mind 
that the denomination is not commensurate with what is de- 
noted by the name, that it is, as in many other cases in lan- 
guage, founded on only a part of the object meant, no serious 
evil will arise from continuing the use of the appellation ; 
probably less evil, indeed, than would arise from attempting 
an innovation on a received nomenclature. 

A Conditional Syllogism, then, is one in which the new 
Judgment or Consequent is derived through the relation of 
the copulas of the Antecedent Judgments ; as, If A is, B is ; 
but A is, therefore B is ; A is B or C ; but A is B ; there- 
fore A is not C. 

§ 72. Inasmuch as every Judgment is essentially an Affirm- 
ative or a Negative, it might be anticipated that Their two 
there would be two modes of mediating a conclu- modes - 
sion through the copula according as it should be affirmative 
or negative. There are, in fact, accordingly, two modes of 
reasoning through the copula — the one is called the Affirm- 
ative, the Ponent, or the Constructive, as, If A is, B is ; but A 
is ; therefore B is ; the other, the Negative, the Tollent, or 



120 PURE LOGIC. 

the Destructive, as, If A is, B is ; hut B is not ; therefore, A 
is not. 

§ 73. We have distinguished two kinds of Quality : — 
Their two Simple Quality, the two complementary kinds of 
kinds: Hy- which are Affirmative and Negative ; and Disjunc- 

pothetical . ,.,.... ~ ,. 

andDisjunc- tive Quality. On this distinction m Quality is 
grounded a distinction of Conditional Syllogisms 
into the two kinds of Hypothetical and Disjunctive. A Hy- 
pothetical reasoning, like a Categorical, thus, always moves in 
Simple Quality ; while, at the same time, it differs from a cate- 
gorical reasoning in that it is mediated through a Judgment, 
not through a Concept. A Disjunctive Reasoning, on the 
other hand, differs from both in that it moves characteristically 
in Disjunctive Quality. 

§ 74. A Hypothetical Syllogism is a Mediate Reason- 
Hypotheticai * n S m which a new Judgment is mediated from a 
ft^^eneSi Hypothetical through the copula of a Condition- 
nature. i n g Judgment. 

The Sumption in this kind of Syllogism is a Hypothetical 
Judgment, or one in which the subject and predicate are 
Judgments, and which accordingly affirms that these two 
Judgments stand in the relation of logical Whole and Part, 
or of Part to Complementary Part to each other, that is, as 
conditioning and conditioned. The Subsumption may affirm 
or deny the Conditioning Judgment ; accordingly the Reason- 
ing may be in either one of two modes, the Affirmative or 
Negative. And the Conclusion will be, accordingly, an affirm- 
ation or negation of one of the members of the Sumption, 
as in the following example : — 

Common Sumption — If A is, then B is. 

Ponent Mode. Tollent Mode. 

Subsumption : But A is ; Subsumption : But B is not ; 

Conclusion : Therefore, B is. Conclusion: Therefore A is 

not. 



REASONINGS. 121 

Common Sumption : If Socrates is virtuous, he merits esteem, 

Ponent Mode. Tollekt Mode. 

But Socrates is virtuous ; But Socrates does not merit 

Therefore, he merits esteem. esteem ; 

Therefore, he is not virtuous. 

In the Ponent or Affirmative Mode the conclusion is from 
the truth of the antecedent to the truth of the consequent ; 
while in the Tollentor Negative Mode the conclusion is from 
the denial of the consequent to the denial of the antecedent. 

We cannot conversely conclude either from the denial of 
the antecedent to the denial of the cqnsequent, or from the 
affirmative of the consequent to the affirmative of the ante- 
cedent, as will be apparent from an example. From the Hy- 
pothetical Sumption : If the sun has risen it is light in the 
hall ; we cannot conclude from a denial of the antecedent 
member that the sun has risen, that it is not light in the hall ; 
for the hall may be light from some other luminary. Neither 
can we any more by affirming the consequent member, it 
is light in the hall, conclude by affirming the antecedent mem- 
ber, the sun has risen. 

It appears, then, that the antecedent clause conditions or 
determines only positively, while the consequent clause con- 
ditions only negatively. The reason of this is, that the 
Sumption must affirm a determination of the consequent by 
the antecedent, or there would be only a negative — a zero — 
upon which to suspend the reasoning. But it is of the very 
nature of this determination that the consequent is conditioned 
by the antecedent. If no consequent is conditioned there can 
be no antecedent conditioning. To deny the consequent is, 
accordingly, to deny the antecedent. But the Sumption does 
not condition the antecedent upon the consequent member ; 
consequently, we are not authorized from affirming the con- 
sequent to affirm the antecedent. 

A regular and perfect Hypothetical Syllogism must con- 
tain three propositions : a Sumption, Subsumption, and Con- 



122 PURE LOGIC. 

elusion. The Sumption must be an affirmative Hypothetical 
Proposition, affirming the agreement between two judg- 
ments. The Subsumption may be affirmative or negative ; 
but it must either affirm the truth of the antecedent member 
of the Sumption, or deny the truth of the consequent member. 
If the Subsumption be affirmative, the conclusion must affirm 
the truth of the consequent member of the Sumption — the 
Ponent mode ; if the Subsumption be negative, the conclu- 
sion must deny the antecedent member of the Sumption — 
the Tollent mode. 

§ 75. As a Hypothetical Judgment may be either simple 
or disjunctive, so the sumption of a Hypothetical 

Two kinds of « „ . , . , . , i. . 

Hypothetical Syllogism may be either simple or disjunctive. 
y ogism. rpkj g g* veg r j ge f a division into the two classes 

distinguished in reference to this quality in the sumption : 
1. The proper Hypothetical, of which we have just given an 
exposition, and, 2. The Hypothetico- Disjunctive, otherwise 
called the Dilemma, as, Whether A is B or is C, D is E ; hut 
A is B or is C ; therefore, D is E. 

The Dilemma was a great favorite with the Sophists, as 
from the complexity of elements that enter into it, a fallacy 
may easily be disguised or veiled from the notice of an 
adversary. It has also received very prominent attention 
from logicians, who, however, have erred in ranking it as a 
coordinate class with Hypothetical and Disjunctive Reason- 
ings. In so far as it is a reasoning, it is purely Hypothetical, 
the derived judgment being mediated independently of the 
disjunction ; it is, consequently, to be ranked as a subdivision 
of Hypothetical Reasonings. 

§ 76. If, when the characteristics of the Hypothetical and 
The Diiem- °^ * n ® Disjunctive Judgment are combined, the dis- 
ma - junction appears only in the consequent or predi- 

cate member, as in the form, If an action be prohibited, it is 
prohibited either by natural or by positive law, the varia- 
tion from the proper hypothetical is not for any purposes in 
thought sufficiently important to demand any special treat-. 



REASONINGS. 123 

ment. But if the disjunction appear in the antecedent or 
subject member, we have a class of judgments of peculiar 
interest and importance. This species is called the Dilem- 
matic Judgment^ being used in the famous reasoning known 
as the Dilemma. Its form is, Whether A is B or is D, E 
is F ; whether it melt or freeze, the road will he rough. We 
have here a disjunction of judgments, not of concepts ; and 
it is the truth of one or the other of the alternative judg- 
ments constituting the antecedent on which the truth of the 
whole judgment rests. The meaning is, either alternative 
judgment, that it will melt or that it will freeze ', involves the 
judgment that the road will he rough. 

This Judgment is properly signalized by the conjunction 
whether •, synonymous with if — or. 

Its forms are various. In the first place, the disjunction 
may be extended to more than two members. If it be 
carried to three, the reasoning is called a Trilemma ; if to 
four, a Teiralemma ; or if to any number more than two, 
generally a Polylemma. The term dilemma, is, however, 
applied to all, whatever the number of disjunct members in 
the sumption. 

In the next place, the disjunction may be either in the 
subject or in the predicate of the sumption, or in both sub- 
ject and predicate. 

In the third place, the reasoning may be either in the Po- 
nent or the Tollent modes. 

In any of the forms, the Subsumption, as in the proper 
Hypothetical Syllogism, either posits the antecedent in order 
in the conclusion to posit the consequent, or sublates the con- 
sequent in order to sublate the antecedent. The reasoning 
accordingly turns on a' judgment, and is mediated through 
that. It is thus a mediate conditional reasoning. 

The true historical Dilemma, as a reasoning which offers 
to an adversary an alternative of propositions, the so-called 
tt horns of a dilemma,'' one of w T hich he must take, is that 
in which the subsumption is a disjunctive proposition. The 



124 PURE LOGIC. 

first and the fourth of the forms given below, are exam- 
ples. 

The following are exemplifications of different forms of 
the Dilemma. 

1. Portent Dilemma with disjunct antecedent: — "Whether 
the blest in heaven have no desires or have desires that are 
fully gratified, they will be perfectly content ; but they either 
will have no desires or will have them fully gratified ; there- 
fore, they will be perfectly content." The reasoning pre- 
sented in this full syllogistic form, would, in ordinary dis- 
course, be expressed in some such compendious way as the 
following : " The blest in heaven, will either have no de- 
sires, or if they have desires, must have them fully grati- 
fied, so that in either case they will be perfectly content." 
The formula of this form is, Whether A is B or G, D is E ; 
hut A is B or G ; therefore, D is E. 

2. Tollent Dilemma with disjunct antecedent : — " If it had 
rained, or if there had been a heavy dew, the walks would 
be wet ; but the walks are not wet ; therefore, there was 
neither rain nor dew." If A is B or (7, D is E ; but D is 
not E ; therefore, A is neither B nor G. 

3. Ponent Dilemma with disjunct consequent : — " If the 
parallelogram be not equal to the triangle, it must be either 
greater or less ; but it is not equal ; therefore, it is either 
greater or less." If A is B, G is D or E ; but A is B ; 
therefore, G is D or E. 

4. Tollent Dilemma with disjunct consequent : — " If man 
is incapable of progress towards perfection, he must be 
either a divinity or a brute ; but man is neither divinity nor 
brute ; therefore, he is not incapable (= is capable) of prog- 
ress towards perfection." If A is B, G is D or E ; but G 
is neither D nor E ; therefore, A is not B. 

5. Tollent Trilemma: — "If mind and matter are not 
essentially diverse, then either they must be absolutely iden- 
tical, or there is no such existence as mind, or no such ex- 
istence as matter ; but neither of these three suppositions 



REASONINGS. 125 

is tenable ; therefore, mind and matter are essentially dis- 
tinct." If A is B, then C is D, or E, or F ; hut is neither 
D, nor E, nor F ; therefore, A is not B. 

§ 77. A Disjunctive Syllogism is a Mediate Reason- 
ing in which a new judgment is mediated through Dis j unctive 
a new judgment removing the disjunction ; as, A is Syllogism. 
B or is G ; hut A is B ; therefore, A is not (7. 

It comes immediately under the second pair of the four 
fundamental Laws of Thought — those of Disjunction and 
of Exclusion. In this respect, it differs from Categorical as 
well as from Hypothetical Syllogisms, neither of which classes 
directly recognizes this pair of Laws. 

It is composed of three propositions, of which the Sump- 
tion is a Disjunctive Proposition ; the Subsumption removes 
the disjunction in the Sumption, which may be effected in 
either of the two ways of affirming or denying, giving rise to 
two modes, the Ponent or Affirmative, and the Tollent or 
Negative; and the conclusion denies or affirms the member 
not subsumed. 

The Sumption of a Disjunctive Syllogism, as ever a Dis- 
junctive Proposition, admits of the three gradations of logi- 
cal opposition: 1. Pure logical contradiction, lying in the 
copula, as, A is B or is not B ; 2. The looser logical contra- 
diction, in which the opposition lies in the terms, as, A is B 
or non-B ; animals are vertebrate or invertebrate ; and, 3. Con- 
trary opposition, as, A is B or C 

The Sumption is necessarily always affirmative, as we can 
conclude nothing from a mere zero of thought ; much less 
from an impossibility in thought, as is the case in the pure 
Contradictory Disjunctive. 

Now, as a Disjunctive Proposition, from its very nature, in 
its strictest form respects two members, either of which may, 
supposably, but only one of which can, actually, be recog- 
nized as true, it is clear that the new judgment — the con- 
clusion — may be mediated through the removal of the dis- 
junction either by affirming, positing, or by denying, sublat- 
zng, one of the two disjunct members. "We may, from the 



126 PURE LOGIC. 

Disjunctive Sumption A is B or is not B, either conclude 
by affirming — positing one member to a denial — a subla- 
tion of the other, or conversely, by sublating one to a positing 
of the other. There emerge, thus, two distinct kinds of 
Disjunctive Syllogisms, 

1. The Affirmative, Portent, or Positing, (modus ponens, 
modus ponendo tollens,) in which one of the disjunct members 
is posited in the Subsumption and the other sublated in the 
Conclusion, as, A is B or ; but A is B ; therefore, A is 
not G. 

2. The Negative, Tollent, or Sublating, (modus tollens, 
modus tollendo ponens,) in which one of the disjunct members 
is sublated in the Subsumption and the other posited in the 
Conclusion; as, A is B or C; but A is not B; therefore, 

a is a 

It is obvious that either of the disjunct members may be 
posited or sublated in the Subsumption ; and that the number 
of disjunct members need not be restricted to two. But in 
case there are more than two, they must be taken as consti- 
tuting but two parts, one part of them being the complemen- 
tary of the other. Thus, if we have a Sumption in the form 
A is B, or 0, or D, or E, and, in the Subsumption, posit B, 
we sublate C, D, and E, which three together make up the 
complementary of B. Or, if we posit B and C, then we 
sublate D and E, which are the complementary of the posited 
part of the disjunct members. The general principle in all 
disjunctive reasoning is that by positing one 'part we sublate 
the complementary part, and by sublating the one part we posit 
the complementary part. 

It will be seen from this exposition of the nature of a dis- 
junctive reasoning, that the removal of the disjunction in the 
sumption is essential. Consequently if there be no such 
removal of the disjunction, although the sumption may be 
a Disjunctive Proposition, we have no disjunctive reasoning. 
Thus the following is not a Disjunctive but a Categorical 
Syllogism : A is B or C; but D is A ; therefore, D is B 
or C. 



REASONINGS. 127 

The Disjunctive Syllogism, moreover, may proceed in either 
quantity, Extensive or Intensive. Unless the special forms 
appropriated to the one or the other of these two kinds of 
logical quantity are employed, the reasoning may generally 
be explicated in either with equal facility. 

The following examples, one in abstract, the other in con- 
crete matter, will sufficiently illustrate the peculiar character 
of a disjunctive reasoning when expounded in the complete 
form of a Disjunctive Syllogism : — 

Common Sumption : A is either B or G or D. 
Ponekt Mode. 
Subsumption : But A is B ; Or, A is either B or C. 
Conclusion : Therefore, A is neither G nor D ; Or, There- 
fore, A is not D. 

Tollent Mode. 

Subsumption : But A is not B ; Or, A is neither B nor O. 
Conclusion : Therefore, A is either G or D ; Or, There- 
fore, A is D. 

Common Sumption : The ancients were in genius either 
superior to the moderns, or inferior, or equal. 

Ponent Mode. 
Subsumption: But the ancients were superior to the moderns. 
Conclusion : Therefore, they were neither inferior nor equal. 

Or, 
Subsumption : But the ancients were either superior or 
equal. 

Conclusion : Therefore, they were not inferior. 

Tollent Mode. 
Subsumption : But the ancients were not inferior. 
Conclusion : Therefore, they were either superior or equal. 

Or, 
Subsumption : But the ancients were neither inferior nor 
equal. 

Conclusion : Therefore, they were superior. 



128 PURE LOGIC. 

It is plain that we may explicate the syllogism in either 
Quantity with equal readiness ; thus, in Extensive Quantity, 
the class ancients is contained under the class superior to 
the moderns, or under the class inferior, &e. ; in Intensive 
Quantity, the attribute notion ancients contains in it the attri- 
bute superior to the moderns, or the attribute inferior, &c. 

§ 78. When the antecedent of a mediate reasoning consists 
of more than two judgments related to each other The Polysyl . 
as wholes and parts, or as parts and complemen- lo s ism - 
tary parts, the reasoning is called a Poly syllogism, also, a 
Chain of Reasoning ; in respect to which other mediate 
reasonings are called Monosyllogisms. 

A Polysyllogism is, in truth, only a series of single syllo- 
gisms, and may always be resolved into as many single 
reasonings as there are middle terms in the series. Thus the 
Polysyllogism C is D ; B is G ; A is B ; therefore, A is D, 
consists of two single syllogisms, there being two middle 
terms B and C, thus: 1°. C is D ; B is C ; therefore, B is 
D. 2°. B is £>; A is B ; therefore, A is D. Or, in con- 
crete matter, the Polysyllogism : An animal is a substance ; 
a quadruped is an animal ; a horse is a quadruped ; there- 
fore, a horse is a substance, may be thus resolved into two 
monosyllogisms ; there being two middle terms, animal and 
quadruped. 1°. An animal is a substance ; a quadruped is 
an animal ; therefore, a quadruped is a substance. 2°. A 
quadruped is a substance ; a horse is a quadruped ; there- 
fore, a horse is a substance. 

It appears from this illustration that the polysyllogism is 
equally valid as the single syllogism. It differs, in fact, from 
a series of single syllogisms in which the conclusion of one 
becomes a premise in another of the series, only in the par- 
ticular that it omits the useless mention of this connecting 
proposition. If, in the example, we simply leave out of the 
single syllogisms the connecting proposition which is the con- 
clusion of the first and the sumption of the second — a quad- 
ruped is a substance — w r e have the polysyllogism as in the 
first presented. 



REASONINGS. 129 

It is obvious, also, that the polysyllogism may equally as 
the monosyllogism move in either quantity, Extensive or In- 
tensive. 

Moreover, the reasoning may be progressive or regressive. 
That is, the single syllogisms which make up the chain may 
either of them be placed first ; the order of statement being 
as truly immaterial as in the case of the premises of a single 
syllogism. If the conditioning syllogism be placed first, we 
have the Progressive chain ; if the dependent syllogism be 
placed first, we have the Regressive chain. In truth, accord- 
ing as we explicate the reasoning in the one or the other 
quantity, we have the Progressive or the Regressive series. 
Thus, if we explicate the example in Extensive Quantity, 
we have the Progressive series : An animal is part of the 
class substance ; a quadruped is part of the class animal ; a 
horse is part of the class quadruped ; therefore, a horse is 
part of the class substance. The first single syllogism here 
furnishes the sumption for the second. But explicated in 
Intensive Quantity, the reasoning, in the order in which its 
parts are stated, is Regressive. Thus : 1. Animal contains 
the attribute substance ; quadruped contains the attribute 
animal; therefore, quadruped contains the attribute sub- 
stance. 2. Quadruped contains the attribute substance; 
horse contains the attribute quadruped ; therefore, horse con- 
tains the attribute substance. Here the conclusion of the first 
syllogism furnishes the subsumption of the second. In other 
words, the order of the two single syllogisms is in this last 
explication reversed, inasmuch as the subsumption is placed 
before the sumption, while in the more natural order it should 
be placed after the sumption. Whether the series is Pro- 
gressive or Regressive, is a matter of no moment, so far as 
the validity of the reasoning is concerned. 

§ 79. The Polysyllogism has been distinguished in respect 

of the form of statement, into two kinds : the Epichirema 

and the Sorites. 

The Epichirema is a polysyllogism in which one or more 
9 



130 PURE LOGIC. 

of the single syllogisms which compose it is immediately 
attached to one of the premises, thus: Animal is a substance; 
a horse is an animal, for it is a quadruped ; therefore, 
a horse is a substance ; ox, A quadruped is a substance, for it 
is an animal ; but a horse is a quadruped; therefore, a 
horse is a substance. 

The attached syllogism, which as in reasoning generally is 
presented elliptically and not in the full verbal form into 
which every thought may be required by our fundamental 
Postulate to be explicated, may obviously be joined to either 
premise or to both, and may itself be a poly syllogism or only 
single. 

The Sorites is- a Polysyllogism in which the single syl- 
logisms which compose it are presented in equally indepen- 
dent relationship to the whole series. It is sufficiently exem- 
plified in the examples given of the Polysyllogism. Indeed, 
it is the regular form, while the Epichirema is the irregular 
form of the Polysyllogism, into which the former may always 
be changed without affecting the nature of the reasoning. 

§ 80. The Polysyllogism, further, may be Categorical or 
Conditional, which may, moreover, be in either form — the 
Sorites or the Epichirema. 

The Categorical species has been sufficiently treated in the 
general exposition already given of the Polysyllogism. 

The Conditional Polysyllogism embraces the two varieties 
of the Hypothetical and the Disjunctive. 

It will be sufficient to give exemplifications of these varie- 
ties without more extended explanations. It is only necessary 
to add, that they may proceed in either Quantity — Exten- 
sive or Intensive ; that they may be Ponent or Tollent ; that 
the series may be Progressive or Regressive ; that the num- 
ber of links in the chain is limited only by the considerations 
of clearness and facility of expression ; and that they respec- 
tively come under the control of the principles which regu- 
late the higher classes of reasoning to which they severally 
belong, and may always be resolved into single syllogisms. 



REASONINGS. 131 

Hypothetical Sorites : If Harpagon be avaricious, he is 
discontented ; if he is discontented he is unhappy ; now 
Harpagon is avaricious ; titer ef ore, he is unhappy. 

Hypothetical Epichirema : If Harpagon is avaricious, 
he is intent on gain ; if he is intent on gain he is unhappy, 
for he is discontented ; now Harpagon is avaricious ; 
therefore, he is unhappy. 

Disjunctive Sorites: A Science is either Pure or Induc- 
tive ; a Pure Science is either Mathematical or Logical ; 
but Astrology is neither Mathematical, nor Logical, nor In- 
ductive ; therefore, Astrology is not a Science. 

Disjunctive Epichirema : All Science is either Pure or 
Inductive ; a Pure Science is either Mathematical or Logi- 
cal, for it treats either of the Conditions of Thought or 
the Elements of Thought ; but Astrology is neither Math- 
ematical, nor Logical, nor Inductive ; therefore, Astrology 
is not a Science. 



PURE LOGIC. 

PART II. 

METHODOLOGY. 
CHAPTER I. 

METHOD IN GENERAL. 

§ 81. " Method in general is the regulated procedure to- 
Method— wards a certain end; that is, a process governed 
what. by rules, which guide us by the shortest way 

straight towards a certain point, and guard us against devious 
aberrations. Now the end of Thought is Truth, Knowledge, 
Science — expressions which may here be considered as con- 
vertible. Science, therefore, may be regarded as the perfec- 
tion of thought, and to the accomplishment of this perfection 
the Methodology of Logic must be accommodated and be 
conducive." 

But while Science, thus, is the proper end of all Thought, 
and Logical Method must have reference to Thought as its 
one end, it is still to be regarded only as the immediate end, 
which may, itself, be modified and controlled by still higher 
ends. In fact, Science or Truth may have its end either in 
itself — in the True, or in the Beautiful, or in the Right and 
Good ; and the Method of Thought will vary in some re- 
spects with this specific remoter end. Still further, the 
Method of Thought will vary with the more specific ends 
under each of these higher governing ends. We may deal 
with Thought for the purpose of acquiring knowledge, or for 



METHOD IN GENERAL. 133 

the purpose of communicating knowledge ; and the Method 
requisite for the Investigation of Truth will so far vary from 
the Method requisite for the Communication of Truth. 

In like manner the Method of Thought, as governed by 
the higher end of guiding to the Beautiful, will vary specif- 
ically, as the particular end is the Contemplation or the Cre- 
ation of the Beautiful. 

So, too, we have a specific variation in the Method of 
Thought, where the governing idea is the Right or the Good, 
according as Subjective or Objective Rectitude or Goodness 
is the particular end. 

It is sufficient to point out here these modifications of 
Logical Method in respect to these several general ends in 
thinking. The full, detailed consideration of them belongs 
either to Modified Logic or to Applied or Special Logic. 
Pure Logic confines itself to the domain of Truth in itself — 
Science for its own sake. 

§ 82. Science, farther, as true or certain knowledge, sup- 
poses two conditions. Of these, the first has a Threefold 
relation to the object known ; the second, to the of s^knee : 
knowing subject. Moreover, it cannot be accepted ^m^isA 
as fully perfected until properly embodied in Lan- Verbal, 
guage. We have thus determined to us the threefold Per- 
fection of Science — Material, Formal, and Verbal. 

Now as Logic is a Science exclusively conversant about 
the form of thought, it would seem that it could take, into 
account only the former of these two elements — the formal 
perfection of thought. And in a certain sense this is a cor- 
rect inference. Only, in fact, so far as the form is necessarily 
dependent on the object of thought, only so far as its formal 
perfection must of necessity regard the matter, does Pure 
Logic look to the matter of Thought. Were Logic to shut 
out from its view all consideration of the matter, of Thought, 
it would be reduced to such meagre proportions as to be un- 
worthy of the name of a science, and barren of all utility ; 
much as would be the case with Geometrical Science if, be- 



134 PURE LOGIC. 

cause a pure formal Science, it were to exclude from its con- 
sideration all distinctions of its object, such as Lines, Surfaces, 
and Solids, Rectilineal and Curvilinear Surfaces, and the 
like. The truth, the objective reality of its matter, indeed, a 
purely formal Science does not regard. The conclusions of 
Mathematical Science are equally sound whether there be 
space or not ; whether space be a proper entity or a mere 
form of our thinking ; whether there be, indeed, extension, 
that is, extended matter in space or not. It only supposes 
this or that in regard to its matter, — space, extension, — as- 
sumes it or accepts it as given to it. So Logic only assumes 
its matter or accepts it as given to it by other sciences. Yet 
inasmuch as, if we think, we must think of something, and 
that something must be viewed as standing in a necessary 
relation to our thought, so thought must be necessarily differ- 
ent, if carried beyond the most shadowy abstractions, as its 
object differs. Logic will then so far regard the matter of 
thought as to see that it is possible to think it and to think it 
correctly. As Thought regards Being as its object, and as 
Being is necessarily apprehended in the two aspects of Sub- 
stance and Cause, and, if apprehended at all, must be appre- 
hended in one of these two aspects, the proper Logical 
Perfection of Thought requires that this twofold considera- 
tion be taken of Being. Logic does not assume it into her 
province to prove the reality of Being as either Substance 
or Cause. She only assumes or accepts it as given to her, 
and deals with it as if real. Her laws are, consequently, 
just as valid to the pure Idealist as to the Realist. But she 
necessarily demands that what is given her be so given as 
that her capacities of receiving may lay hold of it ; and so 
far she must assure herself in regard to Being that it is 
shaped to her capacities, conformed to her nature. Being, 
even ideal Being, can be nothing to Logic, except as appre- 
hended in this seen correlation to her proper functions, which 
are simply and characteristically functions of Quantity, mov- 
ing only in the relations of Whole and Parts. Farther than 



METHOD IN GENERAL. 135 

this, Logic needs to apprehend Being in order to verify, to 
illustrate, to apply her laws. Her growth, if growth she 
could be supposed to have, would be only the shadow of an 
abstraction unless allowed in Being. There could be no illus- 
tration, no exemplification. Moreover, the utility of Logic, 
and well-nigh its whole worth to man, lies in the possibility 
of its being applied to the objects with which he is conver- 
sant. If not so developed as to be readily and habitually ap- 
plied to the realities of human life, logical science could only 
be regarded as a toy, a bubble, brilliant and beautiful it may 
be, but worthless, instead of being, as it should be, the chief- 
est guide and helper to all intellectual growth and culture. 

Logic, then, must so far deal with the matter of Thought 
as to be able to verify its applications to Being, both as Sub- 
stance and as Cause. It must view them, indeed, only in the 
relations of proper Identity and Quantity — of Whole and 
Parts. But it must view the parts of Substance in a some- 
what different light from the parts of Cause. It must regard 
the parts of the former as Attributes in the narrower sense, 
and those of the latter as Effects — Effects in its fullest 
sense. As Thought proceeds differently, although under the 
self-same law r s, when applied to the two respectively, Logic 
must be able to follow these different procedures with assur- 
ance of being right in its regulation of them. 

Logical Science has, for the most part, regarded only Sub- 
stance, and although it has used the term attribute to denote 
whatever can be predicated of a subject, it has in its illustra- 
tions identified the term with the parts of a Substance, and 
has seemed to ignore utterly the parts of a Cause. Indeed, 
the reputed father of the Science, Aristotle, himself seems to 
think Substance and Cause convertible in all predication ; 
and in this he has been followed by subsequent logicians. 
Thus the proposition, " The Romans conquered," is alleged 
to be convertible with the proposition, " The Romans were 
victorious." But this is to confound " action " with " quality" 
the one being predicable only of " Cause," the other only of 



186 PURE LOGIC. 

" Substance." And the obscurities and errors which have 
followed from the confusion have been not less, nor of less 
importance, than those which have followed from the con- 
founding of the two species of Logical Quantity — Compre- 
hensive and Extensive. They are no less serious than what 
might be supposed to follow from confounding lines with sur- 
faces in geometry, as has been done by some who through 
this fallacy have fancied they have solved the great problem 
of the Quadrature of the Circle. 

It will not be amiss to recapitulate the principles which, 
as we have seen, cover the relations of Thought to its 
matter. 

1. The object-matter of Thought is a duality of cognitions. 

2. These cognitions are viewed in Thought only in the 
relation of Same and Different, or derivatively, as Wholes or 
Parts. 

3. Such cognitions as Wholes or Parts are of different 
kinds which, in order to perfect knowledge, Thought must 
distinguish. There are two generic divisions of Wholes — 
(1.) Those of Thought itself. (2.) Those external to Thought. 

4. The Wholes of Thought are either — (1.) Conditions of 
Thought, as the Affirmative and the Negative, which, as Com- 
plementary Parts, make up what may be called The Dianoetic 
Whole ; or, (2.) Products of Thought, the Wholes of Compre- 
hension and Extension, called Logical Wholes. 

5. The Wholes external to Thought are — (1.) Those of 
Forms of Being, called Integrate, comprising the tw r o species 
of Spacial and Numerical. (2.) Those of Being itself, sub- 
divided, in reference to the two modes of Being, into (a.) 
Substantial, and (b.) Causal. 

§ 83. The Material Perfection of Science involves in its 
Two virtues largest import the reality of the matter, as well as 
^erfecUonof ^e correctness of the thought. We distinguish in 
Science — a ]j Science, in all Thought, three elements : the 

Adequateness 4 7 . 

and Accu- object known, the knowing subject, and the act of 
knowledge itself. Now although a science can 



METHOD IN GENERAL. 137 

be regarded as perfect only when these three elements are in 
their respective perfection, only when there is a true matter, 
a true intelligence, and a true knowledge, Logic — Discur- 
sive Logic, as the Science of the Laws of Knowledge as 
Knowledge — dismisses the two related extremes, the perfec- 
tion of the Matter and the perfection of the Intelligence, 
and limits itself to the consideration of the third element — 
that of the relation between them. It leaves to the proper 
Nomology of the Presentative Faculties — the Nomology of 
Perception, the Nomology of the Regulative or Intuitive 
Faculty — to prescribe the conditions of a perfect cognition of 
the matter which it appertains to them to apprehend. Such 
a cognition might be denominated the Material Perfection 
of Knowledge, as importing only that the matter as presented 
by these faculties to the Discursive Faculty is correctly ap- 
prehended by them ; that is, in correspondence with its true 
being. But the Material Perfection of Science which falls 
within the domain of Logic is widely different from this. 
As Thought is the relation between the Thinking Subject 
and the Object Thought, which, it should be remembered, is 
not the original object of the Presentative Faculties, but 
ever a cognition, it has a double aspect, looking both inward 
to the subject and outward to the object. Now, Thought, to 
be perfect in this outward relation — in relation to the cog- 
nition presented to it — must be conformed to its object. It 
must both be conformed to the outer limitations of the mat- 
ter, be conterminous with it, be adequate, filling out the 
entire field of the matter without transcending it ; and it 
must also, in like manner, be conformed to all parts or con- 
tents of the object — must be accurate. These two, then, 
are the two virtues comprised in the Material Perfection of 
Science, so far as it falls within the domain of Logic : — Ade- 
quateness and Accuracy. 

§ 84. The Formal Perfection of Science comprises three 
virtues : — one common to it with other cognitions, as those 
of Perception and Intuition, founded in the very nature 



138 PURE LOGIC. 

of the Intelligence, viz : Clearness ; the second, founded on 

Three vir- the g enei> al characteristic of Thought itself, its 

mafpfrfe?-" relativeness, viz : Congruence, otherwise called 

tionof^Sci- Harmony or Agreement; the third, on the spe- 

cieamess, cific characteristic of this relativeness in Thought, 

Congruence, . . . 

and Distinct- as being that of Whole and Parts, viz : Distinct- 



ness. 

The one Essential Perfection of all Intelligence, viewed 
irrespectively of its relations to its objects, is Clearness. A 
perfect cognition and a clear cognition are convertible ex- 
pressions, if we regard cognition only on its purely formal 
side — cognition simply as cognition. This perfection of 
Thought is determined to it, then, by the very nature of the 
Intelligence of which it is one product. 

But Thought is a relative cognition, being by this attribute 
of relativeness distinguished from other products of the In- 
telligence. That there should be this relation apprehended 
in all Thought is thus indispensable to its perfection. The 
terms, which constitute the factors in this relation, must be in 
correlative or logical harmony — must be congruent. This 
is, indeed, but the principle of Identity in its special applica- 
tion to Method. 

Once more, Thought takes cognizance of its objects only 
in the relations of Identity or Quantity. It deals with 
"Wholes and Parts. Now a clear cognition of the parts of a 
whole as parts, is denominated a distinct cognition. 

Clearness thus respects the outward relations of an object 
of thought — its relations to other objects. Distinctness re- 
spects its internal relations — its relations to the parts of 
which it is composed. 

§ 85. All human science, moreover, stands in a relation of 
dependence, more or less entire, upon Language, 
fectionof If Language must be admitted to be the product 
of Thought, it is yet equally undeniable that Lan- 
guage is the necessary instrument of its progress. Thought 
not only works through Language ; it also exhibits the results 



METHOD IN GENERAL. 139 

of its operations, step by step in its endless working, in lan- 
guage. And, still further, it contemplates, criticises, verifies 
its work, as thus exhibited in language. Its relationship to 
language appears, thus, to be most intimate and vital. It 
becomes important, therefore, to determine, somewhat more 
precisely than we have yet done, this inter-dependence be- 
tween Thought and Language, in order to ascertain the con- 
ditions of perfect science. 

The object of Thought as an activity, we have found to be 
ever a cognition. Thought- begins with a cognition as the ne- 
cessary prerequisite of its movement. Leaving out of view, 
now, those cognitions which are the products of Thought 
itself, and which are presented to it by itself as the objects 
of its activity, the primitive original objects of Thought are 
the simple, individual, or irrelative objects of the Presentative 
and Intuitive Faculties. With these objects given as cogni- 
tions by one or the other of these Faculties, Thought origi- 
nally begins. But simultaneously with these cognitions 
arising in the consciousness, the process of naming, of 
speech-making, begins. It begins, too, there can be no reason 
to question, under the superintendence of the principle of all 
Thought, the principle of Identity ; at least, we must believe, 
in harmony with it. Let us suppose, now, a cognition pre- 
sented through the Perceptive Faculty, through the sense of 
sight, for example, the sun. A name would, under the 
native tendencies of the human soul, at once be given it ; 
and the name as sound, would be one bearing some analogy, 
identical in some respect, with some other accidental modifi- 
cation of the consciousness at the time. We may imagine it 
to be possibly an ejaculation prompted by the joy which the 
first perception of the sun would naturally produce. That 
ejaculatory sound would naturally furnish the materials in 
sound for a name of the sun, because identified with its first 
experience of that object. It is now the name of an indi- 
vidual, simple, in other words, irrelative cognition. But 
we will suppose the moon subsequently to come into the ex- 



140 PURE LOGIC. 

perience, producing the identical effect of joy in kind through 
its common attribute of brightness. It would be named like 
the first — be designated by , the same sound in speech. But 
now the name no longer denotes a single object ; it denotes 
a plurality of objects identified in having a common attribute 

— brightness. It is now the name of a concept, formed 
upon the predicate Base — brightness. We will suppose, 
further, a third object producing the same effect, a star, to 
enter the experience. The name is as naturally extended to 
that. The star is, in other words, gathered into the class on 
the same Base ; and the concept is enlarged in its extension. 
Thus the process goes on indefinitely in this direction. 

But we will now suppose another attribute to be given in 
the experience. The sun is perceived to be round. Bright 
and round are now apprehended as belonging to the same 
subject — sun. The predicates are combined, and a concept 
in comprehension is the result. The name before given to 
the concept in extension is now found to denote more than 
one attribute ; and the name is used now in both senses, 
denoting Comprehension as well as Extension. Other attri- 
butes may be added, and thus the concept may grow in both 
quantities — the limit being always, that in the synthesis of 
subjects there be predicates common to all ; and in the syn- 
thesis of predicates, there be subjects to which they all in 
common belong. The original name first applied to denote 
the irrelative object, sun, thus comes to denote a concept 
embracing an indefinite number of objects having the same 
complement of predicates, and also embracing an indefinite 
number of predicates all concurring in each of the subjects 

— in other words, a Concept with exactly correlative quanti- 
ties of Comprehension and Extension. 

But in the progress of Experience and Thought, another 
parallel process begins. A body enters the experience 
which is bright, and which, therefore, at first might have been 
united with the sun into a concept under that attribute as 
common to both objects, but it is not round. It cannot, 



METHOD IN GENERAL. 141 

therefore, be gathered into the class of bright round bodies. 
A concept is now formed of bodies that are merely bright, 
with no reference to figure ; and a name to signalize the 
union is given to it — say, luminaries. The first object, sun, 
now belongs to two classes, is embraced in two concepts. To 
indicate it, a name is made up by combining so many of the 
predicates as will suffice to distinguish it from other objects 
embraced under the concept. Thus arise modifying words 
or adjectives ; and by the use of them we are enabled to in- 
dicate in language the primitive individual object with which 
the process began, by calling it the sun, or the great heavenly 
luminary. We thus clearly separate it from all other objects 
embraced in sun, regarded as a subject-concept — that is, in 
its Extension — in other words, define it by the use of certain 
adjectives, called, hence, Definitives. In a precisely analo- 
gous way, we indicate the primitive individual attribute or 
predicate. We say the bright sun, meaning that one property 
of the complement of characters that have been gathered into 
the word regarded as a predicate concept, that is, in its 
comprehension, employing here certain adjectives called in 
this case Epithets. Or convenience or occasions of use may 
bring in, during the progress of speech, a new word derived 
from some other language, as Phoebus, or suggested by some 
other accident in experience. And from this word may start 
a new process in word-formation. 

Precisely in the same way the concept-word may be nar- 
rowed to a species only ; that is, to a part of the comprehen- 
sion, instead of being carried through to the individual attri- 
bute. Here, too, new series of word-formations may origi- 
nate. 

Such is the genesis of language, so far as concept-words, 
whether concretes, that is, subject-concepts, or abstracts, that 
is, predicate-concepts, and the thought-element in them are 
concerned. The consideration of the genesis of the sound- 
element in words is foreign to Logical Science. 1 It appears 

1 See Appendix B. 



142 PURE LOGIC. 

from this that it is a gross error to suppose that Language origi- 
nates with general ideas. Such ideas are the product of 
thought alone, and, therefore, presuppose the individual cog- 
nition. Nothing can be conceived more preposterous than 
that the process of generalization, from which alone general 
ideas can arise, precedes the cognition of individual objects 
and attributes. Generalization presupposes, also, the naming 
of these individual objects and attributes. Moreover, the 
instinctive generalization that has gone on in the genesis of 
language, has been step by step, by the addition of one object 
and one attribute at a time. It may be, indeed, that that 
object or attribute may have been a group or an aggregate 
that subsequently has been found to embrace a plurality of 
separable objects or attributes, but when first apprehended in 
thought it must have been viewed as one — as individual. 
To trace back the history of a concept word, whether con- 
crete or abstract, in the expectation of finding a generic or 
comprehensive cognition at the origin, is to proceed in contra- 
diction of the first principles of thought. Bright, for example, 
is now a generic appellation ; but it could have become so 
only by being found, in the progress of Experience, to belong 
to a plurality of objects. It was, if we may assume it here 
to be a primitive word, originally given as a property of an 
individual. It is, also, now, a composite abstract, embracing 
such involved characters as radiant, undulating, sense-im- 
pressing ; but it must have been originally simple, and could 
only in the progress of experience come to be regarded as a 
composite. 

Now it is apparent from this summary view, that only the 
few words which are first applied to designate individual 
objects and simple characters or attributes, come from any 
other faculty than that of thought ; that Thought, as the 
principle of Identity in all acts of the Intelligence, presides 
over the first naming of these ; that these names of individ- 
ual objects and simple attributes, begin at once to pass into 
concepts, which are the pure products of Thought, and even 



METHOD IN GENERAL. 143 

individual objects and simple attributes come to be designated 
by concept words used to modify one another. Thus Language 
comes finally to be made up, to a large extent, of words which 
have been determined as to their meaning and use by Thought. 
But the view we have taken shows, also, that Language is 
not less the instrument than the product of Thought. The 
results of previous processes of Thought are taken as mate- 
rials and conditions of new processes. Thought takes con- 
cepts already formed, and combines them with other con- 
cepts, thus forming new concepts, and still new combinations 
onward indefinitely. Now it is obvious that as the concept 
must always maintain the exact correspondence between the 
two quantities of Comprehension and of Extension, and as 
Thought does not bring up in review all the individual objects 
and simple characters which have in successive combinations 
entered into the concept, there must be great liability to 
error. Moreover, there is a constant tendency for the very 
sake of precision in Thought, to narrow the import of words. 
Thus, for example, the word Thought, itself, formerly included 
in its meaning all acts of the mind, emotions and volitions, 
as well as acts of Intelligence, but now is limited to the acts 
of one of the Faculties of the Intelligence. Still further, 
when we say Thought has shaped Language, we use meta- 
phorical diction. Men, thinkers, individual thinkers, acting 
indeed together in their intercourse with each other, and 
under common regulative principles, have produced all words, 
created all language. Hence the extreme necessity that 
Thought, as it presses its products into verbal forms, should 
be aware of the many liabilities to error, and protect itself 
against them as far as may be, in order to arrive -at its goal 
of truth or perfect science. Only when it has verified its 
incorporation of its products into language expressing cer- 
tain truth, can it be assured of having reached' this its goal. 
In this, is attained the Verbal Perfection of Science, w T hen 
Knowledge, conformed to the realities of things as appre- 
hended by the Presentative Faculties, and shaped into its 



144 PURE LOGIC. 

own essential form by Thought, appears at last in its proper 
embodiment of language. 

To recapitulate these views of the relations of Thought to 
Language : — 

lations of !• The cognitions, attained by the Perceptive 
Language to and Intuitive Faculties, of individual objects and 

Thought; as . -,-,,., 

Product, as ot simple attributes, are named under the guidance 
and as Em-' and prompting of the proper principle of Thought 
bodiment, _ that of Identity. 

2. The concepts, elaborated by Thought out of these 
primitive cognitions, which make up the great body of notion- 
words in a language, are expressed in language in words de- 
rived from the names of those primitive cognitions, and are 
equally under the guidance of Thought. 

3. On the other hand, all the movements of Thought are 
through words ; and all its products attain to permanent life 
only as embodied in words. Language is the Instrument as 
well as the Embodiment of Thought. 

§ 86. The Verbal Perfection of Science, implying its per- 
VerbaiPer- feet embodiment in Language, involves two char- 
Sdrace °, its acters or virtues : — 1. Correctness; 2. Perspicu- 

two virtues ni1 q n pqq 
— Correct- OUSlieSs. 

Pers^cuous- Correctness is founded upon the relations of 
ness. Thought to its outward body, language. It re- 

quires that the thought be truly rendered in the words that 
express it. More specifically, correctness requires - — 

1. That the naming of the primitive cognitions given by 
the Presentative Faculties to ThougGt, be founded on some 
identity cognizable in proper Thought. 

2. That the naming of concepts be founded on the rec- 
ognized identity in respect to their Base, of the subjects or 
of the predicates which are respectively combined to form 
the concept. 

3. That the relations of the Terms in Judgments be ex- 
pressed in such wise as truly to represent the specific charac- 
ter of the Judgment, and, also, the specific nature of the 
kind of whole in which the Judgment moves. 



METHOD IN GENERAL. 145 

Perspicuousness is founded upon the essential quality 
of Thought as Intelligence, viz., Clearness, and requires 
that the Thought appear clearly through the verbal expres- 
sion. 

Subordinate qualities of Perspicuousness are Significance ; 
Perspicuousness Proper, requiring use of unambiguous words 
and right arrangement of relative words ; and Brevity. 

§ 87. It is evident that inasmuch as there are various 
products of Thought, whose perfection must re- Divisions of 
spectively be determined by their bearing these Methodol °S7- 
several virtues of Thought in their modified applications, 
Logic must accommodate its Method to the consideration of 
these virtues in detail, as they pertain to these several prod- 
ucts of Thought. 

The products of Thought, although alike the products of 
the same Faculty, — the Discursive Faculty or Faculty of 
Comparison, whose essential and characteristic function it is to 
identify what is common to a plurality of objects, — vary, as 
we have seen, as different gradations from one another. The 
simplest and most fundamental of these gradations is the 
Judgment. Now, inasmuch as a Judgment is the identifica- 
tion of an attribute or character as belonging to an object, 
the Logical Perfection of a Judgment is attained by securing 
the conditions of an identification of the attribute or charac- 
ter with its object. The determination of these conditions 
wu'll accordingly form the matter of a Methodology of the 
Judgment. 

A Concept, being produced by an act of synthesis, — by 
combining into a unity the several subjects identified with a 
common predicate, or the several characters or attributes 
identified with a common subject, — will attain perfection by 
securing the conditions of such synthesis or combination. 
And Methodology, as applied to this element of 'thought, will 
determine and indicate these conditions. 

A Reasoning, being derived from a Judgment, either by 
an act of Transformation or of Analysis, will attain its log- 
10 



146 PURE LOGIC. 

ical perfection by securing the conditions of this transforma- 
tion and analysis. The Methodology of Reasoning will ac- 
cordingly investigate and point out the conditions of these 
two modes of derivation. 

Logical Methodology will thus consist of three depart- 
ments corresponding with the three Elements of Thought : 
1. The Methodology of Judgments. 2. The Methodology of 
Concepts. 3. The Methodology of Reasonings. 



CHAPTER II. 

METHOD IN SPECIAL. — METHODOLOGY OF JUDGMENTS. 

§ 88. The full Perfection of a Judgment involves the 
several conditions of Material, Formal, and Ver- The Three 
bal Perfection, as these virtues may character- of Perfection 
ize an identification of an attribute with its sub- mentsf" 
ject. 

These three conditions, accordingly, — - 1. That in respect 
of its matter, the predicate be recognized as agreeing with 
the subject ; 2. That in the thought this identity be deter- 
mined or declared in the judgment ; and, 3. That the verbal 
statement correspond with the identity as thought, — are the 
self-evident, as they are the most fundamental, conditions of 
a perfect proposition. 

In regard to the first condition lying in the matter, it may 
be remarked that it is not incumbent on Logic to verify the 
matter that is originally given it as the object of thought. 
But when matter is thus given and the Discursive Faculty 
applies its energy to it, what is given must be treated in con- 
formity with its own nature. Thought must not deal with 
Being as if it were only Mathematical Form. Accepting 
the formula /= 1 as mere formula expressive of the identity 
of every object of Thought with itself, it must not then con- 
vert this form without content into form with content ; in 
other words, surreptitiously foist in Being into this empty 
form, and flatter itself it has proved the reality of Existence. 
In like manner, if its given matter be Substance, it must 
not in the handling of it treat it as if Cause. Thought 
must comprehend its own matter, and must be held respon- 



148 PURE LOGIC. 

sible for the maintenance of its purity throughout all its 
processes. 

Hence the rule that the Judgment be so framed that in 
the matter as given by the Presentative or the Representa- 
tive Faculties, that which is taken as subject or as predicate 
be clearly recognized in accordance with the kinds of whole 
in which the matter is viewed. No rule in Method is more 
fundamental than this, or more wide-sweeping. ' It w T ould be 
impossible to exclude error from a Judgment, incongruence 
from a Concept, or fallacy from a Reasoning, except on this 
condition : that the Judgment admit of a ready reference of 
its terms to its matter as given, so far as the kind of Quantity 
is concerned, for a verification of its truth. While in strict- 
ness Logic takes only what is given, and is concerned purely 
with the form, not with the matter, it must never ignore the 
relationship of form to matter, and must order its procedures 
in harmony with this relationship. The principle of this re- 
lationship is that of Quantity. That we can think any object 
implies that the object contains the principle of Whole and 
Parts and thus answers to Thought, which moves only accord- 
ing to this principle. The two virtues of Thought to be se- 
cured by this Law are those of Adequateness and Accuracy. 
It is the Objective Law of a Judgment, and aims at the 
Material Perfection of Science. 

The next rule is that the identity between the Terms 
affirmed in the Judgment be clearly recognized. This is the 
Subjective Law of a Judgment, and aims at the Formal Per- 
fection of Science. 

- 

The third rule is that the Language in which the Judg- 
ment is embodied be recognized as truly representing the 
thought. This is the Verbal Law of a Judgment, and aims 
at the Verbal Perfection of Science. 

The distinct enumeration of these fundamental Rules of a 
Judgment is important both to correct thinking, and also to 
correction of error in the results of thinking. Only as the 
mind has become habituated to discriminate these three 



METHODOLOGY OF JUDGMENTS. 149 

several kinds or degrees of truth in a proposition — corre- 
spondence of the notions to the terms, agreement between the 
terms, and correspondence of the words to the notions — can 
it proceed safely in the exposition of its thoughts. And only 
as it is enabled readily to distinguish the several ways in 
which error can creep into its thoughts, can it verify them or 
purge them from the error that vitiates them. 

§ 89. The foregoing are the general conditions or rules of 
a perfect Judgment. We proceed to those that Rules of Neg- 
are special. These will vary according to the Disjunctive 
special nature of the several kinds of Judgments. Jud g ments - 
The most general distinction of Judgments is in respect of 
their essential Quality, as Affirmative, Negative, or Dis- 
junctive. The Rules for the Affirmative Judgment are obvi- 
ously the same as those that have been given for Judgments 
as such. The Rule for the Negative Judgment is, that the 
terms of the Proposition be recognized as opposed or differ- 
ent — as non-identical. Nothing need be said in explication 
of this rule, as it is only the negative phase of the rule for 
affirmative Judgments. 

The Disjunctive Judgment presents peculiar difficulties, 
and requires more extended consideration. This Judgment, 
it must be borne in mind, is founded on the third and fourth 
Laws of Thought, the Law of Disjunction and of Exclusion 
or Excluded Middle, which obliges us to think that of two 
contradictory attributes one must, and only one can, belong to 
the subject. The obvious condition of a perfect Disjunctive 
Judgment, then, is that the disjunction affirmed be a true 
contradictory disjunction. 

The liability to error in forming Judgments of this class 
arises from the inadequacy of Language to furnish terms for 
all the contradictory oppositions that may arise in Thought, 
and the resulting necessity of a recourse to the. so-called op- 
position of Contrariety, which gives only a mediate disjunc- 
tion. In this case, to secure that the Judgment be a perfect 
Judgment, the disjunction will need to be carried up into one 



150 PURE LOGIC. 

of contradictory opposition. For illustration, in the Disjunct- 
ive Judgment, Angles are right, acute, or obtuse, we test the 
perfection of the Judgment by applying the principle of 
Contradiction successively to the several pairs of disjunct 
members. We say, first, Angles are right or are not right ; 
then we say, Angles that are not right are acute or obtuse, that 
is, less or greater than right ; and in this way attain a proper 
logical or contradictory disjunction. Only so far as we can 
carry through this contradictory disjunction between the mem- 
bers, can we have the logical basis of a perfect Disjunctive 
Judgment. 

The two Rules, then, which are involved in the conditions 
of a perfect Disjunctive Judgment, are, — 

First, if the disjunction be one of two members, they must 
be recognized as contradictories to each other. 

Secondly, if it be one of more than two members, the 
members must, by being properly paired with each other, or 
with others to be supplied, be reducible to the form of a 
series of Disjunctive Judgments of Contradictory Opposi- 
tion. 

As disjunction in thought and disjunction in the verbal 
expression are expressed in language by the same particles, 
or, nor ; either, or ; neither, nor ; it becomes necessary to ap- 
prehend which is intended. The following proposition is 
equivocal : Consequently space is divided from itself by space, 
or is not divided at all. The disjunction may be interpreted 
to apply to the Judgment, w r hen the meaning will be, Space 
either is divided from itself by space, or is not divided at 
all ; or to the mode of expression, when the meaning will be, 
Space is divided from itself by space, in other words, is not 
divided at all. 

It should be remembered that a perfectly pure disjunction 
can only be in the copula. A either is B or is not B, is not 
always convertible into A is cither B or non-B, in which 
the disjunction is in the terms, the datum of the Judg- 
ment. 



METHODOLOGY OF JUDGMENTS. 151 

§ 90. The second distinction of Judgments we found to be 
grounded on their Modality. The conditions of a 

n -r - • V, ,.,... Rules of 

perfect Judgment imposed by this distinction are Modal judg- 

merits 

that its character as Pure, that is, assertory, or 
as Modal, and if Modal, as Problematic or Apodictic, be 
clearly recognized. The special liability to error here orig- 
inates in the fact that through the imperfections in language 
the modality of the judgment which lies in the copula alone, 
may be covertly slipped over to the predicate. Thus the 
judgment, Alexander may have conquered Darius, is easily 
converted into the proposition, Alexander was a possible 
conqueror of Darius, 1 which is a very different proposi- 
tion ; and although in certain uses the two are equivalent, 
in other uses they would have a very different import. The 
one is a purely concessive proposition, which, from its nature, 
may require no proof; the other is an assertory proposition, 
and proof may reasonably be required of him who puts it 
forward. 

The several species of Judgments given by this distinction 
differ from one another in strength. The Apodictic is the 
strongest, and involves the Problematic and the Assertory ; 
and the Assertory involves the Problematic. The danger, 
therefore, is that what has been problematically enounced 
should be mistaken for an assertory or a necessary judgment; 
or that a mere assertory judgment or enunciation should be 
mistaken for an apodictic or necessary judgment. 

Further, as no sensible symbol, no sight or sound, can ade- 
quately express a purely mental act, and language from its 
felt impotency even forbears often any expression of the act 
of judging, it is to be expected that the distinctions of judg- 

1 It is remarkable, to illustrate this liability, that Sir William Hamil- 
ton calls the proposition, Alexander conquered Darius honorably, a Modal 
Proposition; and as he readily converts it into the form, t Alexander was 
the honorable conqueror of Darms, when the modification is unquestion- 
ably one of the predicate, not of the copula, he concludes that the distinc- 
tion of propositions on this ground of modality is futile. — See Lectures on 
Logic, xiv, page 181. Boston edition. 



152 PURE LOGIC. 

ments in themselves would be left subject to imperfect and 
equivocal means of expression. The forms of language used 
to denote these distinctions are, in fact, borrowed from those 
appropriated to other uses. It becomes necessary, therefore, 
in order to secure correct thought, to weigh carefully the 
language in which it is conveyed ; — to apprehend whether the 
forms used do, indeed, express modality at all, and if so, 
whether that modality is adequately determined in them. The 
distinctions of modality are denoted in the English Language 
by the auxiliaries may or can with their respective tense 
inflections for the Problematic, and must for the Apodictic 
Judgment ; and also by Adverbials, as possibly, probably, neces- 
sarily, and the like. Now all these modal forms may attach to 
the matter thought, or to the Thought itself, and hence arises 
the equivocality in expressing modal distinctions. Thus in 
the Judgment, John may recover in a month, the meaning 
may be that his disease is such as to admit of his recovery, 
and the Judgment itself be strictly assertory. Or, on the 
other hand, the contingency may lie in the Judgment itself. 
Although in ordinary, loose discourse, it may answer equally 
well to connect the contingency with the predicate or with 
the copula, yet correct thinking may often require that the 
distinction be clearly noted. 

§ 91. The third distinction of Judgments is founded on the 

degree which is regarded in the determined aprree- 
Rules of & ° m 

partial ment between Subject and Predicate. 

The conditions of a Perfect Judgment imposed 

by this distinction, are : — 

1. That the Identity affirmed be distinctly recognized as 
Total or as Partial, both in respect of Thought and of Verbal 
Expression. 

2. That if the Identity be Partial, the precise part of the 
containing whole, whether it be in the Subject or in the 
Predicate which the affirmation respects, be distinctly recog- 
nized. 

§ 92. The fourth distinction of Propositions is into the two 



METHODOLOGY OF JUDGMENTS. 153 

species of Categorical and Hypothetical, according 

as the whole regarded in them is an object or potneticai 

truth. Judgments. 

The first condition, then, prescribed by this distinction, is 
that the Judgment be recognized as belonging to the one or 
to the other of these species. 

The difficulty here will be found chiefly with the Hypo- 
thetical Judgment, in discriminating accurately wherein the 
identity affirmed in the Judgment between the terms lies, as 
the real nature of the Judgment is obscured by the form in 
which it is expressed, as well as by the name which has in- 
aptly been given to it. It should be fully understood that 
there is nothing more conditional or hypothetical in the nature 
of a Hypothetical Judgment than in any other. The simple 
import of every such Judgment is that the truth expressed 
in the subject, or, as it is called, the first or antecedent mem- 
ber, involves or conditions the truth of the predicate or con- 
sequent member. Now, inasmuch as for the most part Prop- 
ositions in discourse are only expressions of a partial identity 
between the subject and the predicate — only affirm that 
some one part of the subject is identical with the predicate, 
or some one part of the predicate is identical with the sub- 
ject, or, it may be, some one part of the subject is identical 
with some one part of the predicate, — the liability to error in 
the so-called Hypothetical Judgment is far greater than in 
the case of a Categorical Proposition, inasmuch as it is more 
difficult to identify the parts of a truth than the parts of an 
object. The hypothetical form of the Proposition, moreover, 
disguises the true nature of the Judgment, and so increases 
the liability to error. 

This dissection of the Hypothetical Proposition, accord- 
ingly, prescribes the following conditions of a Perfect Hypo- 
thetical Judgment : — 

1. It must be clearly apprehended in its true nature as a 
Judgment, the terms of which are Truths or Judgments, not 
simple objects — not Concepts nor Integrate Wholes. 



154 PURE LOGIC. 

2. The specific parts in the terms — in the Antecedent and 
the Consequent Members — between which the identity af- 
firmed lies, must be distinctly recognized, as also the truth of 
these members as themselves judgments. 

3. It is further necessary to recognize whether the Judg- 
ment is in the relation of Whole and Part, or in that of Part 
and Complementary Part. 

To illustrate the application of these conditions, we will take 
the Hypothetical, proceeding in the relation of Whole and 
Part : If there he a God, the world is governed by Provi- 
dence. The first condition requires that we distinctly recog- 
nize the proposition as one in which the terms, here called 
the Antecedent and Consequent Members, are Truths or 
Represented Judgments, assumed pro hac vice to be true ; as 
meaning, in other words, that the truth that a God is, con- 
tains in it the truth that the world is governed by Providence. 
The second condition requires that we recognize the parts of 
these several truths which are asserted in the proposition to 
be identical. We do this by analyzing the terms of the first 
member, that God is, and discovering that one part of the 
notion God, is providential ruler. 

To illustrate these Rules in a Hypothetical proceeding in 
the relation of Part and Complementary Part : If virtue 
is voluntary, vice is voluntary. First, we recognize the 
proposition as meaning that The truth that virtue is volun- 
tary, involves in it the truth that vice is voluntary. Next, 
we recognize those parts in the members which are identical. 
The attribute of morality belongs alike to virtue and vice, as 
parts complementary of each other. In that respect they are 
the same — they are both moral. 

It will have been observed that the Hypothetical Judg- 
ment occurs often in discourse as a true reasoning, as a kind 
of Enthymeme, one of the premises being suppressed. The 
terms of the Judgment, in fact, stand in the relation to each 
other of a conclusion to a premise ; and they are hence ap- 
propriately called respectively the Antecedent and Conse- 
quent members of the Judgment. 



METHODOLOGY OF JUDGMENTS. 155 

§ 93. The Fifth distinction of Judgments is into Extensive 
and Comprehensive or Intensive Judgments, being Ruleg of 
founded on the Logical Quantity of their terms. f™^^Jj 
The conditions of a perfect Judgment given by ^?£ i( j al 
this distinction is that its Logical Quantity be dis- 
tinctly apprehended, so that it be recognized whether the 
subject or the predicate is the containing whole. This can 
always be effected by changing the form of the Judgment so 
as to put it into the phraseology distinctive of the two Quan- 
tities. Thus the proposition, Man is rational, expressed in 
Comprehensive Quantity, would read : The whole, man, con- 
tains in its complement of attributes the part or attribute 
rational. In Extensive Quantity : The part or species, man, 
is contained under the whole or genus, rational. 

§ 94. The sixth distinction of Judgments is founded on 
the kind of Whole that is thought in the matter ?^ es of , 

° Judgments 

of the Judgment, whether an Integrate, a Substan- in different 

£ /^cti , Wholes of 

tial, or a Causal Whole. Matter. 

This distinction imposes this condition of a perfect Judg- 
ment: that the kind of Whole expressed by the terms be 
clearly recognized, whether an Integrate Whole, the parts 
of which lie out of each other ; or a Substantial Whole, the 
parts of which permeate each other as simply congruent ; or 
a Causal Whole, the parts of which permeate each other, not 
only as congruent, but also as determined through the same 
Causal Whole. Thus Parts in a Mathematical Whole are 
Parts of that Whole ; Parts in a Substantial Whole are 
Parts in or under that Whole, according as the Whole is a 
Comprehensive or Extensive Whole ; Parts of a Causal 
Whole are Parts through that Whole. In the Mathematical 
or Integrate Whole, the nexus is simply aggregation ; in a 
Substantial Whole, the nexus is substance ; in a Causal 
Whole, it is cause. 

§ 95. To recapitulate the conditions of a Perfect Proposi- 
tion, that is, of a true Judgment truly expressed, it is neces- 
sary to recognize it — 



156 PURE LOGIC. 

1°. As to its Verbal Form, as having perfect correspondence 
between the Thought and the words. 

2°. As to its Quality, whether Identifying, or Differencing, 
or Disjoining in contradictory or in contrary opposition. 

3°. As to its Modality, whether simply Assertory, or Prob- 
lematic, or Necessary. 

4°. As to degree of its Identification, whether Total or 
Partial, and if Partial, in respect of what part. 

5°. As to the logical Gradation of its terms, whether Judg- 
ments, Concepts, or Integrate Wholes ; in other words, 
whether Hypothetical or Categorical. 

6°. As to the logical Quantity of its Terms, whether if 
Logical, an Extensive or an Intensive Whole ; or, if Mate- 
rial, whether an Integrate, a Substantial, or a Causal Whole. 



CHAPTER III. 

METHODOLOGY OF CONCEPTS. 

§ 96. The Perfection of a Concept as a Synthesis of the 
homologous terms of two or more Judgments iden- The three 
tified through the sameness of the other term, in- of perfection 
volves three conditions, corresponding respectively m Conce P ts - 
with the three fundamental virtues of perfect science. 

The first condition is, that the terms, which being combined 
form the concept, be the homologous terms of Judgments hav- 
ing their other terms the same. This is the Objective Law 
of the Concept, giving it its Material Perfection. 

The second condition is, that the concept itself be thought 
in its perfectness as a Whole in its relations both to other 
Concepts and to its Parts. This is the Subjective Law of a 
Concept, giving it its Formal Perfection. 

The third condition is, that the verbal body of the Concept 
truly represent the matter as thought in it. This is the 
Verbal Law of a Concept, giving it its Verbal Perfection. 

§ 97. The Objective Law of the Concept enjoins two things : 

1°. That the terms combined to form the Con- 
cept be recognized as homologous terms. iveLawofa 

2°. That these terms be recognized as from ° ncep ' 
Judgments having the other terms the same — that is, that 
the Base be recognized. 

The validity and binding force of these two rules will be 
recognized at once, as they are seen to be but the applica- 
tion of the principle of Identity, or, as it is in this ' relation 
denominated, the Law of Congruence, to Concepts. 

The terms united to form the Concept must be homologous ; 



158 PURE LOGIC. 

— that is, must be either all subjects or all predicates. To 
attempt the union of subjects with predicates in the same 
notion, would be to attempt the union of things unlike in 
respect of the same relation in which they are to stand in the 
union — to identify non-identities, or opposites. 

Further, it is plain that not all homologous terms can be 
synthesized into a concept. The principle of Identity that 
governs all thought requires that the terms be related to one 
another by having a common element for each of the other 
terms of the primitive Judgments, which common element we 
have called the Base of the Concept. Thus if the Concept be 
in Extensive Quantity, the subjects must be all identified in 
the Judgments with the same predicate, as its Base. If, on the 
other hand, the concept be one in Comprehensive Quantity, 
the predicates which compose it must be all identified in 
previous Judgments with the same subject, as its proper 
Base. 

It is to be observed, moreover, that in Thought a term is 
not the same unless it be thought in the same kind of Whole. 
We may suppose terms which can be identified in Judgments 
with the same subject or the same predicate, but in different 
kinds of whole ; they cannot be synthesized into" a Concept 
any more than solids and surfaces. Thus we have as true 
Judgments : Man is biped ; Man is soul and body ; Man 
thinks ; but the incongruence in the kinds of Wholes in which 
the thought moves, forbids the synthesis of the predicates 
into a Concept. 

In order, therefore, to the more thorough-going determina- 
tion of the question whether two given terms are congruent 
or not, the kind of whole to which the concept belongs 
should be carefully distinguished. In a Mathematical or In- 
tegrate Whole, the parts of which lie out of each other, in- 
congruent parts are, of course, only such as overlap each 
other. Circles and rectilineal figures cannot thus be united 
in thought as making up any polygon, for they must overlap 
each other. They are incongruent parts. Head and Bones 



METHODOLOGY OF CONCEPTS. 159 

are incongruent parts of Body ; Fiber and Leaf, of Plant ; 
Thought and Predicate, of a Sentence ; Sanction and Pro- 
mulgation, of Law. These several Wholes, conceived as In- 
tegrate Wholes, are not made up of such kinds of Parts as 
appear in each of these pairs. The parts in each couplet 
overlap each other. Thus a circle may be contained in a 
polygon ; but its complement, the part or parts which with the 
circle make up the polygon, cannot be rectilinear. Head is 
a part of Body regarded as an Integrate Whole ; but Bones 
are not the complement of Head, nor do they with any other 
part make up such complement. And a similar view must 
be taken of the other examples. The parts are not comple- 
mentary of each other. They are, in reference to the same 
Whole, incongruent, inasmuch as in any attempt to fill out 
the given whole, some part must overlap some other. 

In a Substantial Whole, in which the Parts permeate each 
other, the incongruence will lie in the opposite nature of the 
Qualities that are ascribed to the Subject ; or, inasmuch as 
a Relative Whole may be represented in Thought under the 
analogies of a Substantial Whole, in the opposite nature of 
the Relations ascribed to the Subject. Thus, Blue and Red; 
Round and Angular ; Rough and Smooth ; Stiff and Flex- 
ible ; Thick and Thin; Skillful and Indolent; Moral and 
Deceitful, are respectively pairs of Opposite Incongruent 
Parts. So far as they creep into the same Thought, the union 
is fatal to the Thought. 

In a Causal Whole, the incongruence will lie in the union 
of parts which are not determined by the same cause. The 
distinctive relationship of the parts in these several wholes 
as before observed, is, to some extent, indicated in the prepo- 
sitions that are commonly used to express it. In an Integrate 
Whole, the parts are parts of the whole; in a Substantial 
Whole, they are in or under the whole ; in a Causal Whole, 
they are through the whole. Thus Integrant Parts of the 
notion Man, are Body and Limbs; Substantial Parts are 
Rational and Animal ; Causal Parts are Virtue and Vice. 



160 PURE LOGIC. 

All the effects which may be through the cause are proper 
parts of a Causal Whole, as all the properties which are con- 
tained in an object conceived as Substance, are proper parts 
of that substance. Man, thus, as Free cause, that is, Moral, 
contains virtue and vice through this freedom. These are 
Congruent Parts of the Causal Whole, Man as Moral ; Incon- 
gruent Parts would be Virtue, Vice, Suffering. So of the 
notion Sculptor as cause, Incongrueiit Parts would be Statur 
ary, Relief, Carving, Mosaic, the last being not through a 
Sculptor as such. 

It might be thought that the Objective Law of the Con- 
cept, as thus interpreted, would not be adequate to secure in 
full the Material Perfection which it proposes. But in 
strict logical consideration, the matter of a Concept is given 
in the Judgments from which it is derived ; and consequently, 
the law of its formation cannot be expected to go back of 
the Judgments which are its proper matter. The question 
whether our concepts, which make up, as we have seen, the 
great body of our notion-words in discourse, do actually an- 
swer to the external realities to which we unconsciously in 
speaking and thinking refer them, is one indeed of momen- 
tous concernment to us. Are these notions which we fabricate 
so freely in our thought, all unreal, having no correspond- 
ences in the world of being around us ; are our references 
of them to this objective world all illusory and deceptive ; 
or, on the other hand, is the outer world constituted on the 
same principle of Identity which underlies and governs all 
Thought, having its likes and its unlikes, its samenesses and 
its differences in infinite variety and extent, exactly an- 
swering to the infinite variety and extent of our Thought- 
products — is the universe around us resolvable into the self- 
same species and classes which appear in our concepts, so 
that, if our thinking be legitimate, we may rest assured that 
there are corresponding species and classes of things about 
us ? — these are questions, indeed, of most vital interest to 
us ; but they lie properly out of the domain of Pure Logic. 



METHODOLOGY OF CONCEPTS. 161 

Yet two observations may without impropriety be introduced 
here. 

First, the forming of Concepts, as, for instance, the gather- 
ing into classes is determined by the special occasion or object 
of our thinking. Logic does not prescribe that, any more 
than does Arithmetic prescribe to what object we shall apply 
its processes — to the calculation of Interest, or the compu- 
tation of Magnitudes. Logic only prescribes the proper 
movements of Thought, when Thought is required for any 
work to which it is fitted. We must not then expect that 
the outer world of realities should be broken up into pre- 
cisely such parts as the occasions of our thought may happen 
to require. In other words, we must not expect that the 
lines of separation in the various objects of the actual world 
are distinctly drawn just where the uses of our thought may 
lead it to draw them, — that there are so many classes of 
animals or vegetables or minerals in the universe as we may 
in legitimate Thought choose to enumerate. Classifications, 
Concepts, vary with the occasions of our thinking, with the 
advancement of Science ; the world around is constant in 
the relationships of its multiform contents. Generalizations 
in Science, thus, will sometimes be founded on essential 
attributes, sometimes on extrinsic attributes or relations ; 
sometimes on one of these essential attributes, or of these 
relations, sometimes on another. Even systems of natural 
science will vary, in respect of the principle of classification 
and consequently in respect of the entire method of the par- 
ticular system, with the advancements of the science. Ac- 
cepting the doctrine that classification in the science of nature 
must be, " so far as it is accurate, the literal interpreter of 
the creative plan of God," 1 and must rest, therefore, on in- 
trinsic or essential attributes, — as those of proper Quality as 
in plan of structure for higher classifications, and of those of 
Quantity as in complicity of plan for lower, — we yet see that 
even here there is room for much diversity among naturalists 

1 L. Agassiz, Methods of Study in Natural History, chap. iv. 
11 



162 PURE LOGIC. 

in their perfectly logical systems of generic arrangement, 
until science reaches its ultimate limit. " The plan of God 
in creation as expressed in organic forms " has remained the 
same unchanged through the successive systems of Aristotle, 
Linnaeus, Cuvier, Baer, and their co-workers in this great 
field of science, and will abide the same through all the 
changing systems of classification as they go on in the ever- 
advancing progress to a perfect science which shall be founded 
on an accurate apprehension of all the facts, and a congruent 
representation of them in forms of classified knowledge, con- 
venient for the uses of man in his perfected nature and 
condition. 

Secondly, that there is a true correspondence between 
legitimate Thought and the universe of Being with which it 
is conversant, it is most irrational to question. Even if there 
be not, it is to us just as if there were; and therefore it is 
unreasonable to call the correspondence in question. Fur- 
ther, it can never be proved that there is no correspondence ; 
for thought is impossible where there are no relations — no 
correspondences. To presume such want of correspondence 
so as to throw the burden of proof upon the party that af- 
firms the correspondence, is but most unjustifiable arrogation 
— the presumption, whatever there may be, being all on the 
other side, so that the skeptic must be held to make good his 
doubt, that is, must invalidate his own skepticism. Still 
further, reason and revelation agree in teaching that legiti- 
mate thought has its counterpart in the realities of its objects. 
Reason postulates one universe, one Creator, <one principle 
of creation — unity in the wondrous diversity, harmony in 
the infinity of parts, sameness in endless difference ; and so 
we are taught every created thing is created " after his kind." 
This principle of kind, of identity in creation, stamped upon 
it at its origin, and maintained ever by the same Divine 
agency, never contradicting itself, that first brought it into 
being, is the fundamental principle in the universe of things, 
exactly answering to Thought. There is a true kind, a 



METHODOLOGY OF CONCEPTS. 163 

species in things, that never perishes, forbidding transforma- 
tion into other kinds, and commingling of kinds, so that if 
such appear, we instinctively and truly recognize them as 
monstrosities, prodigies, which we forbear to account for till 
we attain a higher point of view from which to look out on 
the orderly arrangement of things that appear around us — 
a higher, purer light in which to study the well-ordered 
universe of God. Language, in its various forms, as shaped 
by the most cultivated portions of the human race, attests 
the general acquiescence of men in the correlativeness of 
thought and specific identity in nature. The words genus, 
hind, kin, can, know, and numerous others, all of one stock, 
and similar in the different dialects of the great Indo-Euro- 
pean family, connect causative power, intelligence, and specific 
identity in clearest and closest relationship. Things are alike 
because the creatures of the same causative power ; things 
correspond to our thoughts, because we and they are products 
of the same power and all are akin to it. In this are grounded 
alike the necessary outward condition of all science and the 
universal instinct of science in- man. Without this corre- 
spondence between Thought and Being, science is an empty 
form ; and the innate aspiration for science is a cheat and a 
lie. Accepting this correspondence with a natural and over- 
powering faith, man through the identities cognizable and 
validated in thought rises surely and successfully along the 
identities of creation, upward into the unity of the single 
creative power in the universe, and attains perfect science. 

§ 98. The Subjective Law of a concept respects the 
thought side, as the objective law respects the TheSubject- 

, . ., „ , . , n , T , .«. ive Law of a 

object side, of this product of the Identifying Concept. 
Faculty. It prescribes the conditions of a perfect cognition 
in a concept so far as they respect the thinking subject. 

The two virtues of a cognition lying in the nature of 
Thought itself, are Clearness and Distinctness — Clearness 
constituting the perfection of a concept regarded as one 
whole in relation to other wholes ; Distinctness being its per- 



164 PURE LOGIC. 

fection regarded in relation to its own parts. Inasmuch as 
these are exhaustive complementary views in thought of a 
thought-cognition — as we can take no third view of it be- 
yond the view of it as a part in relation to other comple- 
mentary parts, and the view of it as a whole in relation to 
its own parts — these are the only two virtues which constitute 
its perfection as a Thought. 

The Subjective Law of a Concept, accordingly, enjoins — 

1. Clearness, or that the concept be recognized as distin- 
guished from all other concepts. 

2. Distinctness, or that the concept be recognized as to the 
several parts of which it is composed. 

The process by which Clearness is attained is called Defi- 
nition. 

That by which Distinctness is attained is called Analysis. 

" To Leibnitz we owe the precise distinction of concepts 
into clear and distinct, and from him is borrowed the follow- 
ing illustration. In darkness, the complete obscurity of 
night, we see nothing- — there is no perception, no discrimi- 
nation of objects. As the light dawns, the obscurity dimin- 
ishes ; the deep and uniform sensation of darkness is modi- 
fied ; we are conscious of a change ; we see something, but are 
still unable to distinguish its features; we know not what 
it is. As the light increases, the outlines of wholes begin to 
appear, but still not with a distinctness sufficient to allow us to 
perceive them completely ; but when this is rendered possible, 
by the rising intensity of the light, we are then said to see 
clearly. We then recognize mountains, plains, houses, trees, 
animals, etc., that is, we discriminate these objects as wholes, 
as unities, from each other. But their parts — the manifold 
of which these unities are the sum — their parts still lose 
themselves in each other, they are still but indistinctly visi- 
ble. At length, when the daylight has fully sprung, we are 
enabled likewise to discriminate their parts ; we now see dis- 
tinctly what lies around us. But still we see as yet only the 
wholes which lie proximately around us, and of these only 



METHODOLOGY OF CONCEPTS. 165 

the parts which possess a certain size. The more distant 
wholes, and the smaller parts of nearer wholes, are still 
seen by us only in their conjoint result, only as they concur 
in making up that whole which is for us a visible minimum. 
Thus it is, that in the distant forest, or on the distant hill, we 
perceive a green surface ; but we see not the several leaves, 
which in the one, nor the several blades of grass, which in 
the other, each contributes its effect to produce that amount 
of impression which our consciousness requires. Thus it is, 
that all which we do perceive is made up of parts which we 
do not perceive, and consciousness is itself a complement of 
impressions, which lie beyond its apprehension. Clearness 
and distinctness are thus only relative. For between the 
extreme of obscurity and the extreme of distinctness, there 
are in vision an infinity of intermediate degrees. Now, the 
same thing occurs in thought. For w T e may either be con- 
scious only of the concept in general, or we may also be 
conscious of its various constituent subjects or attributes, or 
both the concept and its parts may be lost in themselves to 
consciousness, and only recognized to exist by effects or rela- 
tions which indirectly evidence their existence. 

" The perfection of a notion is contained in two degrees or 
in two virtues, viz : in its clearness and in its clearness 
distinctness ; and, of course, the opposite vices of ^ity asl™~ 
obscurity and indistinctness afford two degrees or Conce P ts - 
two vices, constituting its imperfection. A concept is said 
to be clear, when the degree of consciousness by which it is 
accompanied is sufficient to discriminate what we think in and 
through it, from what we think in and through other notions ; 
whereas if the degree of consciousness be so remiss that this 
and other concepts run into each other, in that case the no- 
tion is said to be obscure. It is evident that clearness and 
obscurity admit of various degrees, each being capable of 
almost infinite gradations, according as the object of the 
notion is discriminated with greater or less vivacity or pre- 
cision from the objects of other notions. A concept is ab- 



166 PURE LOGIC. 

solutely clear % when its object is distinguished from all other 
objects ; a concept is absolutely obscure, when its object can 
be distinguished from no other object. But it is only the 
absolutely clear and absolutely obscure which stand opposed 
as contradictory extremes ; for the same notion can at once 
be relatively or comparatively clear, and relatively or com- 
paratively obscure. Absolutely obscure notions, that is, con- 
cepts whose objects can be distinguished from nothing else, 
exist only in theory ; an absolutely obscure notion being, in 
fact, no notion at all. For it is of the very essence of a 
concept, that its object should, to a certain degree at least, be 
comprehended in its peculiar, consequently in its distinguish- 
ing, characteristics. But on the other hand, of notions ab- 
solutely clear, that is, notions whose objects cannot possibly 
be confounded with aught else, whether known or unknown 
— of sueh notions a limited intelligence is possessed of very 
few, and, consequently, our human concepts are, properly, 
only a mixture of the opposite qualities — clear or obscure 
as applied to them, meaning only that the one quality or the 
other is the preponderant. In a logical relation, the illustra- 
tion of notions consists in the raising them from a prepon- 
derant obscurity to a preponderant clearness, or from a 
lower degree to a higher. So much for the quality of clear- 
ness or obscurity considered in itself. 

" But a Clear concept may either be Distinct or Indistinct \ 
The Distinct- the distinctness and indistinctness of concepts are 
Sadness" therefore to be considered apart from their clear- 
of concepts. negs and obscurity. 

" We have seen that a concept is clear, when we are able 
to recognize it as different from other concepts. But we may 
discriminate a whole from other wholes, we may discriminate 
a concept from other concepts, though we have only a con- 
fused knowledge of the parts of which that whole or of the 
characters of which that concept is made up. This may be 
illustrated by the analogy of our Perceptive and Representa- 
tive Faculties. We are all acquainted with many, say a 



METHODOLOGY OF CONCEPTS. 167 

thousand individuals ; that is, we recognize such and such a 
countenance as the countenance of John, and as not the 
countenance of James, Thomas, Richard, or any of the other 
nine hundred and ninety-nine. This we do with a clear and 
certain knowledge. But .the countenances, which we thus 
distinguish from each other, are, each of them, a complement 
made up of a great number of separate traits or features ; 
and it might, at first view, be supposed that, as a whole is 
only the sum of its parts, a clear cognition of a whole coun- 
tenance can only be realized through a distinct knowledge of 
each of its constituent features. But the slightest considera- 
tion will prove that this is not the case. For how few of us 
are able to say of any, the most familiar face, what are the 
particular traits which go to form the general result ; and yet, 
on that account, we hesitate neither in regard to our own 
knowledge of an individual, nor in regard to the knowledge 
possessed by others. 

" Continuing our illustrations from the human countenance : 
we all have a clear knowledge of any face which we have 
seen, but few of us have distinct knowledge even of those 
with which we are familiar ; but the painter who, having 
looked upon a countenance, can retire and reproduce its like- 
ness in detail, has necessarily both a clear and distinct knowl- 
edge of it. Now, what is thus the case with perceptions and 
representations, is equally the case with notions. "We may 
be able clearly to discriminate one concept from another, 
although the degree of consciousness does not enable us dis- 
tinctly to discriminate the various component characters of 
either concept from each other. The Clearness and Distinct- 
ness of a notion are thus not the same ; the former involves 
merely the power of distinguishing the total objects of our 
notions from each other ; the latter involves the power of 
distinguishing the several subjects, the several attributes, of 
which that notion is the sum. In the former the unity, in 
the latter the multiplicity, of the notion is called into relief." 

§ 99. The term Definition is used in a wider and looser, or 



168 PURE LOGIC. 

in a narrower and stricter sense. The general process it- 
Definition- se ^ which it denotes, as applied to various objects, 
its kinds. j s a ] so variously modified. 

As the object of all definition is clearness, which is a qual- 
ity variable in degree, the term- definition is naturally em- 
ployed to denote processes that imply more or less clearness, 
from its lowest degree in mere indication, when by any pecul- 
iarity whatever, even of the most accidental kind, we sep- 
arate one object from another in our view of it, up to com- 
plete logical definition, which entirely bounds out the object. 
The process, again, may be applied to words, to concepts, or 
to any cognition of the Presentative Faculties, viewed in the 
relation of Whole and Part. As applied to words, the proc- 
ess is called Verbal or Nominal Definition. This is effected 
either by synonymous words or expressions, or by indicating 
the etymology of the term to be defined. The term concept, 
thus is defined synonymously as a notion, and etymologic- 
ally as that in thought which is taken with something else ; 
breakfast as morning-meal, or as that by which we breakfast ; 
definition as dilucidation, or as the act of bounding or limit- 
ing off. 

As applied to concepts and carried out to completeness in 
order to perfect science, it is called Logical Definition. 

As applied to cognitions other than concepts, it is called 
variously Dilucidation, Description, or Definition, with or 
without modifying words. 

In its application to an Integrate Whole, we have exempli- 
fications of its use in Mathematical Definitions ; as a Sector 
is mathematically defined to be a portion of a circle bounded by 
two radii and the arc interrupted between them. Such defini- 
tions have the completeness of a proper logical definition. 
They completely separate the object from its complementary 
part. An approximation to this logical completeness is at- 
tained in the definition of the Fore-arm, thought as part of 
an Integrate Whole, as that part of the human body bounded 
by the wrist and the elbow. More vaguely and incompletely 
is Head defined as the upper portion of the body. 



METHODOLOGY OF CONCEPTS. 169 

In its application to Substantial Wholes, when the differen- 
cing element must be found in an attribute by which it is dis- 
tinguished from other substances, it may be exemplified by 
the definition of man as substance, that is, rational animal — 
a definition, as will be seen, that corresponds with the process 
in a proper logical whole. The only difference is, that here 
the denning members, rational animal, are viewed as real, 
not as thought, attributes. Parts of a Substantial Whole, that 
is, attributes, may be defined by differencing them from com- 
plementary attributes of the same substance. 

In its application to a primitive cognition, viewed as a 
Causal Whole, definition is the separation of one cause from 
other causes by a differencing effect, or of one effect from the 
complementary effect of the same cause. Thus, heating is 
defined as the effect of the Sun in expanding bodies ; expand- 
ing being the effect which differences heat from other causal 
agencies of the sun. 

Logicians, it may be observed here, have vaguely distin- 
guished three kinds of Definition — Verbal or Nominal, Real, 
and Genetic. A Verbal Definition is the elucidation, the 
rendering clear of the term or object through its name. 
Thus, a Verbal or Nominal Definition of Concept would be, 
That in thought which is taken with something else. A Real 
Definition of Concept would be, A synthesis of the homolo- 
gous terms of two or more judgments with the same base. 
A Genetic Definition would be, A product of Thought aris- 
ing from the synthesis of homologous terms, &c. A Verbal 
Definition thus elucidates — renders cle:\r — through the 
Word ; a Real Definition through the Substance ; a Genetic 
Definition, through the Cause producing. 

§ 100. The process of proper Logical Definition consists es- 
sentially in recognizing the object defined as a part ^Irition 
in distinction from other like parts of a larger log- its nature.' 
ical whole ; that is, in distinction from its complementary part. 

It is Extensive or Comprehensive according as Definition 

either Ex- 

the concept is viewed in the one or the other of tensive or 
these kinds of Logical Quantity. sive! Pre cn " 



170 PURE LOGIC. 

The nature and validity of this distinction require no il- 
lustration. It is important to enounce it articulately, that in 
undertaking the process of definition the mind may move 
intelligently and freely. As the same name is ordinarily 
applied in Language to a Concept made up in either Quan- 
tity, it becomes the more necessary to determine at once in 
defining in .which the concept is to be viewed, whether as 
a subject-concept or a predicate-concept. Definition in Ex- 
tension respects the subjects of which the concept is com- 
posed ; Definition in Comprehension, the predicates or attri- 
butes. 

It will be sufficient to exemplify the process in each kind 
of Quantity. In Extension, then, to define will be to dis- 
criminate the concept from all coordinate concepts ; as the 
whole here is evidently the genus made up of the concept to 
be defined, and the coordinate species. We attain extensive 
clearness, then, in a concept of a right-angled triangle when 
we discriminate it from all coordinate triangles. We attain 
clearness in the concept man, regarded as part of the Ex- 
tensive whole, animal, when we discriminate it from all non- 
rational animals ; in the concept hope, when we recognize it 
as complementary of fear, in the class of emotions called 
desires. 

In a Comprehensive Whole, clearness is attained by a 
recognition of that character or that complement of charac- 
ters in the concept which it has as peculiar to itself, and not 
in common with other concepts. Thus we attain clearness 
in the concept of a right-angled triangle in comprehension, 
when we view it as possessing the peculiar property of having 
one of its angles right ; of man, when viewed as rational, 
and thus making up with the generic property of a brute, the 
total comprehension of rational animal. We fasten attention 
here on the attribute ; while in attaining extensive clearness 
we look at the subjects of which the attribute is predicated. 
As for the most part terms may be construed in either quan- 
tity, the results attained by the definition will so far be ex- 
pressed in similar terms. 



METHODOLOGY OF CONCEPTS. 171 

The examples given have been indiscriminately in contra- 
dictory and in contrary opposition, and also in positive and 
in negative characters. The strictest logical definition will 
proceed in contradictory opposition — accordingly will be 
dichotomous, or through the two sections of Part and Com- 
plementary Part, expressed logically as A and non-A, these 
two contradictories making up the proper whole of Thought. 
Plato's definitions are characterized as of this form — dichot- 
omous or bi-sectional, proceeding in contradictory opposi- 
tion. We evidently attain strict logical clearness when we 
thus discriminate a concept from its complementary part. 
Now, as in the case of any concept there may be recognized 
many kinds of parts standing in this relation of being com- 
plementary to it, that is, as making up with it so many kinds 
of wholes, it is obvious there may be as many perfect defini- 
tions of the same concept as there are different kinds of 
wholes in which it is a part. Plato's definition of man as 
bird without feathers, is beyond criticism, if the whole be 
taken as biped, so long as only feathered and unfeathered 
beings are known to belong to this class ; for it discriminates 
perfectly man as part of this whole from its complementary 
part. The so-called Aristotelian definition of man as an 
animal walking on two feet, is just as obnoxious to criticism 
as Plato's, and no more so. How this should be is suffi- 
ciently shown in the mode of forming concepts, if, at least, 
we take into view, also, in connection with this, the inade- 
quacy of language to signalize by a distinct word every pos- 
sible synthesis of subjects more or less, or of predicates more 
or less, on any Base more or less composite. What shall be 
the particular whole in which the concept to be defined shall 
be viewed, and consequently, what shall be the definition, 
depends then on the occasions of use. A moral philosopher 
would define man in one way ; a physiologist in another ; 
a political economist in a still different way; and so on, 
and each variously on the varying occasions of his dis- 
course. The process as a movement of Thought remains 



172 PURE LOGIC. 

ever the same — discrimination as part from the comple- 
mentary part. 

But as such movement it is properly in its first step only 
dichotomous, or by discrimination of one part as complement- 
ary. As, however, in contrary opposition generally, so here 
the thought may move on by successive definitions in the 
strict Platonic method, till we attain the degree of clearness 
required. Or we may abridge the process by leaping at once 
to the results of such continued dichotomous definition, just 
as the arithmetician, when the two factors of seven and nine 
are given, leaps to the product sixty-three, without going 
through the entire process, step by step, of adding seven 
units to other seven, and seven more to those, and so on. 

Further, we may define indifferently by positive or by 
negative characters, as we may discriminate man from its 
complementary part, brute, either by the positive character 
rational, or the negative character not-brute or not-irra- 
tional. Evidently what is positive in respect of one part is 
negative in respect of the other part. The movement of 
Thought is indifferent from the one or the other, and the 
same in both. The occasions of discourse, however, gener- 
ally, and of preference, demand the positive. It is hence, 
from the occasions of discourse, that the rule springs which 
prohibits definition by negative characters. 

The convenient and logically sound rule which directs us 
to define by naming the next higher genus and the specific 
difference, has the recommendation of being dichotomous, 
and, by an easy process of conversion, of being explicable in 
either Quantity. Thus the definition of man, as rational 
animal, may be interpreted : Man is of the genus animal, 
and the species rational ; or, Man has the generic attribute 
of animal, and the specific attribute, of rational. Or as de- 
fined by the naturalist, as bi-manous or two-handed mammal, 
it may mean : of the genus mammal, and species bi-manous ; 
or, having the generic character of mammal, and specific 
character of bi-manous. Obviously, however, the rule has 
relation only to proper concept wholes. 



METHODOLOGY OF CONCEPTS. 173 

§ 101. The conditions of Distinctness in a concept are, 1. 
That the kind of parts to be distinguished be first 

* ° Distinctness j 

recognized ; and, 2. That each of these parts be its condi- 
clearly discriminated from the other parts. 

If a still higher degree of distinctness is required than 
that which is given in the discrimination of the first set of 
parts, then each of these parts may be treated as new wholes, 
in which successively distinctness is to be attained. The 
process will be the same as in distinguishing the first set of 
parts. 

Logical Analysis, then, will consist of the two processes, 
first, of recognizing the kind of parts to be attained in the 
Analysis ; and, secondly, of separating into these parts. The 
first is the necessary antecedent condition of analysis ; the 
second is the analysis itself. 

§ 102. The first Law of Distinctness requires that the 
kind of parts, whether Material Parts, as Integrate, Sub- 
stantial, or Causal, or proper Logical Parts, as Extensive or 
Comprehensive, which are to be distinguished, be recognized. 
For the fuller distinctness, indeed, the parts of each of these 
kinds may be discriminated. Thus, the concept Man, may 
be distinguished into the Integrant Parts of Head, Body, 
and Limbs ; or into the Intensive Parts of Rational and 
Animal; or again into the Extensive Parts of Black, 
Tawny, and White; or the Causal Parts of Loving and 
Hating, But in any case the kind of Parts to be discrim- 
inated must be recognized. The necessity of this Law it is 
unnecessary further to illustrate. 

§ 103. The particular kind of parts to be discriminated 
having been recognized, the next step is to effect Analysis; 
the distinction. This is Proper Analysis. This itskinds - 
part of the procedure will vary with the kind of parts, 
giving rise to so many subordinate kinds of processes. 

That process by which Distinctness is attained in In- 
tegrant Parts may be called Dissection ; also, Formal Anal- 
ysis ; 



174 PURE LOGIC. 

That by which Extensive Parts are obtained is called 
Division ; 

That by which Intensive Parts are obtained is called Par- 
tition ; 

That by which Causal Parts are obtained may be called 
Resolution ; also, Evolution, or Causal Analysis. 

It will not escape notice that one kind of wholes is omitted 
in this enumeration of the processes of analysis — that of 
Substantial Wholes. The reason is, that while the ground 
of distinction exists, yet language does not enable us to dis- 
tinguish except by tedious circumlocution to which quick 
thought and speech will not submit, the real from the thought 
characters of an object of thought — actual properties from 
thought attributes. We should, accordingly, be forced to use 
the same terms, and lay out the same rules for analysis in 
Substantial Wholes as for analysis in Comprehensive Wholes. 
With this intimation of the reality of the distinction, and of 
the consequent necessity in the strictest thought of observing 
it on supposable, if rare, occasions, to avoid perplexity, 
analysis in Substantial Wholes is formally omitted, its nature 
and laws being readily gathered from the exposition of anal- 
ysis in Comprehensive Wholes. 

§ 104. There is one general Law of Analysis applicable 
Law of Com- to all the subordinate processes alike. It is the 
pieteness. general Law of Adequacy appearing here in the 
specific form of the Law of Completeness requiring that all 
the Parts in the given Analysis be recognized. The neces- 
sity of this is obvious. So far as the Analysis is incomplete 
some one or more parts being omitted from the recognition, 
the cognition fails in distinctness. Besides this, it must of 
necessity be partial and one-sided, and positive error will be 
the result. For example, if in analyzing Faith as a Chris- 
tian virtue, I recognize only the characters of Intellectual 
Belief, and Sentiment of the Heart, leaving out all Moral 
Disposition, Purpose, or Will, I make it a merely involun- 
tary state, and, of course, exclude from the notion all free- 
dom, all responsibility, all morality. 



METHODOLOGY OF CONCEPTS. 175 

The practical importance of a careful observance of this 
Law of Logical Analysis is to be seen in the fact that by far 
the greatest part of erroneous opinion in all departments of 
knowledge arises from the incomplete apprehension of the 
objects of knowledge. Most dissensions in science and in 
belief would be ended by a complete survey of all the con- 
stituent elements of the matter in dispute. It is mainly be- 
cause the parties look, one at one element, the other at 
another, and each to the exclusion from his view of some 
element or character important to a correct opinion, that any 
dissension arises. 

§ 105. Passing now to the subordinate processes of Log- 
ical Analysis, the first, Formal Analysis or Dis- Dissection: 

• 1 1 • 1 1 • • IT ltS tW0 

section, is that which gives as its result Integrate kinds. 
Parts. These are of two kinds — Spacial and Numerical. 
The distinctive characteristic of each kind is that the parts 
lie out of each other. The fundamental condition of a cor- 
rect analysis here, accordingly, being that no part overlap 
another, we have the comprehensive Law of Formal Analysis 
or Logical Dissection that it proceed from a single principle ; 
that, for instance, but one point of departure in lineal, one 
line in superficial, one plane in solid dissection, be taken ; 
and in numerical parts, one unit of separation. Thus in dis- 
secting tree regarded in simply lineal extent, to take, as one 
part, that below the ground, and as another, that between 
the branching of the roots and the branching of the boughs, 
would vitiate the process, as giving parts that overlap each 
other. So to analyze the United States of America as a 
spacial extent by taking the Atlantic States, the Pacific 
States, the Lake States, the Gulf States, and the Mississippi 
Valley States, even if it were complete, would be incorrect, 
for the lines of dissection cross each other, giving overlap- 
ping parts. So to dissect hope into expectation, desire, and 
pleasure, is vicious, inasmuch as pleasure is not attained by 
the same line of dissection as the other parts. It overlaps 
both. 



176 PURE LOGIC. 

So in Numerical Parts, to dissect a dollar into shillings 
and dimes would necessarily give overlapping parts ; or to 
separate solar light into full splendor, cloudiness, moon- 
light, and twilight, the unit of Degree of Intensity not being 
apprehended, the parts overlap one another; or to distin- 
guish merit as perfect, average, fair, and zero, the third dis- 
tinction of degree not corresponding with the other three. 

§ 106. The second kind of Logical Analysis is that of 
Division, which gives, as its proper result, the 
Extensive Parts of a Logical Whole ; — in other 
words, the objects contained under the whole which must 
here ever be regarded as a genus or class, that is, a subject- 
whole. 

The first step in Division is to recognize the specific kind 
of parts that are sought in the Analysis. From the very 
nature of a subject-concept, that may have as its Base a plu- 
rality of attributes, there may be as many modes of division, 
each giving its own set of parts, as there are different attri- 
butes synthesized in the Base. Thus, man is a subject- 
concept with a Base of the two intrinsic attributes, rational 
and animal ; and the concept may be analyzed into rational 
parts, as cultivated and barbarous ; learned and unlearned; 
intellectual, sentimental, and practical; or into animal 
parts, as tall and short ; white, tawny, and black ; sanguine 
and bilious, and the like. The concept has likewise a Base 
of manifold extrinsic attributes, or attributes of Relation, 
which will furnish so many other modes of division and 
sets of parts ; as European, Asiatic, &c, in relation to coun- 
try or place ; antediluvian and post-diluvian ; governors 
and governed, and the like. An analysis that should pre- 
sent parts of these various kinds, taken indiscriminately and 
confusedly, would obviously be of no worth, as it would be 
without logical method. We must then, as the first step in 
division, apprehend the attribute in the Base of the concept 
in reference to which the analysis is to be made. The at- 
tribute selected for this purpose is called the Principle of 



METHODOLOGY OF CONCEPTS. 177 

Division. Thus the Division of man into cultivated and bar- 
barous has for its principle of division the attribute cultivated, 
being comprehended in the more comprehensive attribute 
rational ; that of man into white, tawny, and blach, is color, 
beings an attribute comprehended in animal. A Division, 
it is seen thus, is effected simply by adding an attribute 
to the Base of a Subject-concept, or Extensive Whole, as by 
adding to rational animal the attribute cultivated, or black, 
we obtain corresponding divisions of the concept man. 

The first and the only proper logical division is dichoto- 
mizes ; giving the two parts, one having the attribute which 
forms the principle of division, the other not ; as man is of 
the two species, cultivated man and not cultivated, that is, 
barbarous man; angles are right angles, and angles that 
are not right. But generally a farther division is required, 
and in the enumeration of the parts those that are negative 
are not specially mentioned, but are represented in the sub- 
ordinate divisions. Thus instead of a division of man in 
respect of Color, first into white and not white, and then 
not white into the two colored species, tawny and black, 
the division is made at once into the three varieties ; and 
angles are divided into right, acute, and obtuse. The three 
parts thus obtained are in looser language denominated 
coordinate, inasmuch as each is complementary of the other 
two. In such case the more comprehensive attribute is the 
principle of division ; as color and magnitude respectively 
in the examples given. In the same way there may be any 
number of parts. 

The first thing, then, to be done, in effecting division, is to 
recognize the principle of division, or the attribute in respect 
of which the division is made. This being done, the one law 
of division is — 

That all the coordinate, that is, complementary parts, given 
by the principle of division, and none others, be distin- 
guished. 

12 



178 PURE LOGIC. 

This comprehensive Law comprehends the following par- 
ticulars : — 

1°. That none but parts — individuals or species — con- 
tained under the given Whole, be taken. 

2°. That no objects or parts be taken which are not 
strictly coordinate with one another under the adopted prin- 
ciple of division. 

3°. That subordinate objects or species be apprehended as 
contained under the super-ordinate. 

4°. That all the coordinate species be distinguished. 

§ 107. The third kind of Logical Analysis is that of Par- 
tition, which gives as its proper result the Com- 
Partition. * & r r 

prehensive Parts of a Logical Whole ; in other 

words, the characters or properties, inherent or relative, that 
make up the whole. The parts in this species of whole 
permeate each other, and are comprehended in the whole. 

The first step in Partition is to recognize some one char- 
acter or property as that which shall determine the kind or 
class of properties sought in the Analysis. What that char- 
acter shall be it is not the province of Logic to prescribe ; 
that is to be determined by the object proposed in the Anal- 
ysis, the consideration of which belongs to Rhetoric or the 
Art of Discourse. Logical Science cannot discriminate be- 
tween the characters or properties that make up a concept, 
as to their relative importance. It can only discriminate 
them as Intrinsic or Extrinsic ; as Conflicting or Congruent ; 
as Involving, or Involved, or Coordinate ; for it cannot tran- 
scend the relationship of Whole and Part. 

Some one particular character or property having been 
thus selected which shall determine the set of characters to 
be taken as making up the concept, the Law of the Analysis 
itself will be derived from the indicated relations of the 
character to the Whole and to the other characters. This 
Law is — 

That none but coordinate characters, and all of them, be 
distinguished. 



METHODOLOGY OF CONCEPTS. 179 

This general Law contains the following particulars : — 

1°. That none but actual characters be taken. 

2°. That no connective characters be taken. 

3°. That involved characters, if distinguished at all, be 
apprehended as contained in the involving character. 

4°. That all the coordinate characters be distinguished. 

§ 108. The Fourth kind of Logical Analysis is that of 
Ke solution, otherwise called Evolution and „ , '. 

sv 7 a 7 . i . i . i Resolution. 

Causal Analysis, which gives as its proper results 
the Causal Parts ; in other words, effects as parts of the con- 
cept viewed as Cause. 

The first step here is to recognize the kind of effects into 
which the concept is to be resolved by apprehending some 
one effect, which with all the others shall make up the com- 
plement of effects through that Cause. Here it should be 
remembered that, from the imperfectness of Language, the 
same name may denote Causes of widely variant effects. 
Thus Man is a name of a Causal agency operating in 
many conceivable different spheres ; as, for instance, mate- 
rially, as counterpoising more or less weight ; chemically, as 
forming by decomposition, nitrogen, carbon, and other chem- 
ical elements ; organically, as breathing, digesting, &c. ; spir- 
itually, as thinking, desiring, willing, and the like. The 
cause in counterpoising, it is obvious, is not the same as in 
breathing, or in thinking. It becomes necessary in order to 
Distinctness in a Causal Whole to apprehend first the kind 
of effects which constitute it, which is done by taking some 
one effect as the determining one of the set of effects to be 
attained in the Analysis. 

This being done, the Comprehensive Law of Causal Anal- 
ysis for attaining Distinctness is — 

That none but coordinate effects, and all of them, be dis- 
tinguished. 

This Comprehensive Law comprises the following partic- 
ulars : — 

1°. That none but actual effects of the given Cause bo 
taken. 



180 PURE LOGIC. 

2°. That no effects be taken which are not strictly coordi- 
nate with one another. 

3°. That derivative effects be apprehended as contained 
through the original effect from which they are derived. 

4.° That all the coordinate effects be distinguished. 

§ 109. The Verbal Law of a concept divides itself into 
two parts, one determined by its relation to the Thought ex- 
pressed in it, the other by the nature of verbal expression. 

I. The Verbal Law of a concept requires that the Ex- 
pression be exactly conformed to the Thought to be expressed. 
This involves — 

1°. That the Expression contain the exact Thought ; 

2°. That it contain all the Thought ; and — 

3°. That it contain no more than the Thought. 

The necessity of a careful observance of these laws rests 
chiefly on the fact that Language is at best an inadequate ex- 
pression of Thought. It furnishes but a single term for a 
great multiplicity of thoughts. Hence the necessity of choos- 
ing, in the first place, the fittest terms for expressing the 
Concept and the parts contained in the Analysis; and, in 
the second place, when the term is not exactly adequate to 
the Thought, of modifying it so as to make the thought and 
the expression exactly coincident. 

One application of this part of the general Verbal Law 
of the Concept is of especial interest and importance. It 
respects the verbal expression of the quantity of the concept. 
The importance of a distinct recognition of this application 
of the law originates in the fact that Language ordinarily 
fails to distinguish in the form of the word the kind of quan- 
tity which is intended. The word tree, for example, may be 
used to denote an Extensive, an Intensive, or an Integrate 
Whole ; — to denote a class of objects, a complement of 
attributes, or a certain individual object. When such words 
are used without modifying words to indicate the quantity, 
they may be taken in either one of these several meanings ; 
and when they are repeated in the same general movement 



METHODOLOGY OF CONCEPTS. 181 

of thought in different relations, there is great liability to 
confusion and error, which can be detected, perhaps, only 
through a discrimination of these several kinds of quantity. 
Logicians even, for a single exemplification, have often failed 
to recognize the difference between the expression, No man 
is immortal, and the proper negative proposition, Man is 
not immortal. They class and treat them both as alike uni- 
versal negative judgments. But there is a most material 
difference in the import of the two propositions. Man, in 
the first proposition, is necessarily to be construed as an In- 
tegrate Whole; while man, in the other proposition, is a 
Class Whole. How easily error may creep into a continuous 
movement of thought, through the loose employment of 
words of this kind, may be seen in an example of a fallacious 
reasoning. Thus : Man is not philosopher ; Newton was a 
man ; therefore, Newton was not a philosopher. The truth 
of the sumption, interpreting the term man as a class whole, 
is unquestionable. Equally so is the truth of the subsump- 
tion. Yet the reasoning is fallacious, being, in fact, an in- 
stance of that kind of fallacy to be explained in the sequel, 
called the fallacy of four terms. Palpable as the error is 
here, it is easy to see that in the progress of continuous dis- 
cussion the fallacy might readily creep in. The familiar 
rule of formal logic requiring the distribution of one term in 
a reasoning is aimed, in part, against this sophistry in some 
of its forms. 

II. The Verbal Law of a Concept requires, in the second 
place, that the verbal expression conform to the laws of ex- 
pression. This involves — 

1°. That the expression be significant. 

2°. That it be perspicuous. 

3°. That it be brief. 

The first of these particulars prohibits all unmeaning 
terms, all needless repetitions, all tautological expressions. 
Significance should characterize the whole and every part of 
the expression. 



182 PURE LOGIC. 

The second prohibits the use of ambiguous, obscure, and 
figurative terms ; and also requires such a structure as the 
settled principles of language impose in order to perspicuous- 
ness. 

The third prohibits all unnecessary words, and also peri- 
phrastic expressions not necessary for accuracy and ade- 
quateness. 



CHAPTER IV. 

METHODOLOGY OP REASONINGS. 

§ 110. The triform perfection of Thought generally, Mate- 
rial, Formal, and Verbal, requisite to perfect science, im- 
poses upon the Reasoning process as a derivation from one 
or more Judgments the three Laws which we have distin- 
guished as the Objective, the Subjective, and the Verbal. 
We will consider the application of these Laws to the differ- 
ent forms of Reasoning under each Law in order. 

Before entering upon this consideration, however, it is 
proper to recall a distinction of methods already Probation 
stated, founded on the different ends for which ga^n dis?" 
thought is exerted. We have distinguished the tinguished. 
two ends of attaining truth and of communicating truth — 
here appearing specifically as those of Investigation and 
Probation. The process of thought in the two methods is es- 
sentially the same ; but the movement is generally and charac- 
teristically in opposite directions. Thus, in attaining truth, 
in investigating, we begin with the proper logical antecedent 
— with the premises ; while in communicating truth, in pro- 
bation, we ordinarily begin with the conclusion. This dif- 
ference, however, is not one of strict logical concernment. 
The movement in investigation is that which is most proper 
for logical consideration ; and to verify thought in probation, 
the doctrine of which belongs properly to Rhetoric, it be- 
comes necessary, therefore, to reverse the movement, so that 
the conclusion, which in argumentation is ordinarily placed 
first, shall stand in its true logical position after the ante- 
cedent. As we shall see, many of the fallacies ordinarily 



184 PURE LOGIC. 

considered in systems of Logic, being purely fallacies of pro- 
bation and not of investigation, belong to Rhetoric. 

It may be added here, that in probation the thought is 

generally presented but in part, as in the Enthymeme, in 

which one premise is suppressed. To verify the thought, 

Logic requires that it be filled out in all its essential parts. 

§ 111. The Objective Law of a Reasoning 

ObiGctivG 

Law of requires that the Antecedent be distinctly recog- 

easomngs. ^^ gg ^ Q -^ f orm &n j i m p 0r t. 

The Antecedent in a Reasoning, it will be recollected, is 
the Judgment, or the Judgments, which are given, from which 
the Consequent or Conclusion is to be thought out in the 
Reasoning. It is the proper matter or datum in the process, 
and must, consequently, in order to perfect science, be ac- 
curately and adequately apprehended. 

This Law, then, presupposes the perfection of the Judgment 
or Judgments which form the Antecedent as the datum of 
the Reasoning. It prescribes as additional requisites to per- 
fect science — 

1°. That the Antecedent be recognized," whether as Simple 
or as Composite, that is, be recognized as to the number of 
Judgments of which it is made up. 

2°. That the specific character of each Judgment in the 
Antecedent be recognized in its Quality, whether Affirmative, 
Negative, or Disjunctive ; in its Modality, whether Assertory, 
Problematic, or Apodictic ; in its Degree, whether Identical 
or Partial ; in its Form, whether Categorical or Hypotheti- 
cal ; in its Logical Quantity, whether Extensive or Compre- 
hensive ; in its Material Quantity, whether Integrate, Sub- 
stantial, or Causal. 

3°. That the Verbal Expression be recognized as correctly 
and unequivocally rendering the Thought, and in a form 
appropriate to the Reasoning process, or at least reducible to 
such form. 

The logical soundness of these rules it would be superflu- 
ous to vindicate at length and in form ; but the importance 



METHODOLOGY OF REASONINGS. 185 

of forming the habit of thus weighing in each integral part 
the datum of a reasoning, can hardly be overrated. It is 
only necessary to add that while it is not difficult to form 
the habit, so that instinctively and unconsciously as it were, 
the precise matter of the reasoning shall be so fully appre- 
hended as to bring to light any defect or ground of fallacy, 
this can be only by a conscious separate attention at first to 
each essential part of the Antecedent. 

The applications of this Law, so far as they are peculiar 
to any one kind of reasoning, will be considered under each 
one, and in connection with its Subjective Law. 

§ 112. The Subjective Law of a Reasoning respects the 
movement of Thought itself in deriving the con- _ , . .. 

° & Subjective 

elusion or consequent from the Antecedent. It Law of 

, , Reasonings. 

will vary under its more general twofold form in 
the two different relations of Whole to Part, and of Part to 
Complementary Part, with the particular kind of Reason- 
ing. We will accordingly consider the Law in its various 
forms of application to the different species of Reasoning in 
order, beginning with Immediate Reasonings in their several 
forms of Conversion, Quantitative Restriction, Modal Restric- 
tion, Transference, Disjunction, and Composition ; and con- 
tinuing with Mediate Reasonings in their several species of 
the Syllogism, Categorical and Conditional, and the Polysyl- 
logism. 

Inasmuch, however, as fallacious thinking generally, if 
not always, is occasioned by the complication of divers simple 
processes in one, it becomes necessary to premise one gen- 
eral rule of high importance to correct thought. 

§ 113. In every case of the intermingling of several proc- 
esses of Thought in the same general movement, , 

° & 7 Law of 

the attainment of assured Truth requires that each Complex 

i i i ■ ■ . i. - .i-i Thought. 

process in the complex thought be distinguished 
and verified through its entire progress. 

No perfectly simple process of thought, perhaps, even with 
the dullest intelligence, can mislead or err. It is only when 



186 PURE LOGIC. 

processes are blended together and the thought becomes in- 
tricate that error or fallacy is possible. The proper and the 
only certain and universal cure is the separate recognition 
and verification of each distinct process that enters into the 
complex movement. 

The enunciation of this general Law will preclude the 
necessity of multiplying specific rules for all the different 
kinds of complex reasoning. It will be sufficient here to 
exemplify the Law in reference to these complications in a 
very general way. 

Conversion is often combined with Restriction, whether in 
Quantity or in Modality, and also with Transference. Logi- 
cians have accordingly distinguished so many different kinds 
of Conversion with tabular forms, showing when inference is 
possible, when not, and on what conditions, with as much 
reason for any practical utility, as if a mathematician should 
tabulate all the possible combinations of addition, subtraction, 
multiplication, and division in any arithmetical process, for 
directing how to compute in each. We may, indeed, gener- 
alize the statement, by enouncing that Immediate Reasonings 
intermingle in all possible combinations, not only with one 
another, but also with Mediate Reasonings of all kinds, sub- 
ject only to the general laws of Thought. Examples of the 
former kind are Conversion per accidens, as, Convertend, A 
is B ; Converse, some B is A, where Conversion is com- 
bined with Quantitative Restriction : Conversion by Contra- 
position, as, Convertend, A is B ; Converse, no Non-B is A, 
where Conversion is combined with Transference. Exam- 
ples of the latter kind are in a kind of Epichirema, as, B is 
A ; C is B, for it is non-D ; therefore, G is A ; or in concrete 
matter : Vice is odious ; Avarice is a vice, for it is unsympa- 
thizing ; therefore, avarice is odious. 

In the same way, Mediate Reasonings are combined with 
one another. One form distinctly treated by logicians, and 
already noticed, is the Hypothetico-Disjunctive, or Dilemma. 
So in the Sorites manifold combinations of the several proc- 
esses are possible within the limits of legitimate Thought. 



METHODOLOGY OF REASONINGS. 187 

To assure certainty in all such instances of complicated 
reasoning, the rule to verify each distinguishable process by 
its own conditions, is the one simple and universally efficient 
rule. At first, as in arithmetical computation, the procedure, 
being thus step by step, will necessarily be slow ; but soon 
the mind acquires power to analyze and verify the most com- 
plicated processes as it were by instinct, precisely as after 
practice it reaches by one leap in multiplication the product 
from given simple factors, without going through the many 
additions involved, or attains the result of manifold simpler 
processes in higher applications of numerical principles. 

§ 114. In Logical Conversion, which consists in the simple 
transposition of the terms of a Judgment, the one 

,£. , D . , . "• ,. & . Subjective 

condition or a perfect derivation or reasoning is, Law of con- 

version 

that the quantity of the terms be not changed in 
the transposition. 

In this reasoning the Quality of the Judgment is not af- 
fected ; the derivation respecting simply the terms. Now 
every Judgment being essentially an identification of two 
objects of thought, it is a matter of indifference to Thought 
in which direction the movement takes place ; whether we 
say A = B, or B = A. If we may say the one, the very 
nature of Thought authorizes us to say the other also. The 
problem in Conversion is this : Having one term given as 
subject and the other given as predicate, how with the main- 
tenance of the integrity of the Thought we may transpose 
these terms. We could, evidently, do this as freely in 
Thought generally as we do in Algebraic equations, were it 
not that for the most part the language of Thought, its nota- 
tion, is not as unequivocal as that of mathematical science. 
The Judgment Man is mortal cannot as securely be con- 
verted as we convert an Algebraic equation by transposing 
the terms, because it is but a partial Judgment, whereas all 
Algebraic equations are properly Identical Judgments. It 
means only that one of the characters that make up the 
notion man, is identical with mortal ; or that man is identical 



188 PURE LOGIC. 

with one of the parts that make up the class mortal. When 
thus interpreted, the conversion becomes as simple and as 
certain as in Algebra. This, then, is the one condition of 
Simple Conversion : that no more and no less be expressed 
by the terms after the transposition than was thought in them 
before. 

Subjective § 115. In Quantitative Restriction, the one con- 

sultative dition of P erfect Thought is, that the quantity 
Restriction, thought be restricted in both terms in equal degree. 

The only difficulty to be encountered in this kind of reason- 
ing is one exactly analogous to that in Conversion. If from 
the Judgment Man is rational animal, we wish to derive a 
Judgment restricted in the subject only, as, this man, Ameri- 
can men, &c, are rational animal, we do it without fear of 
fallacy, because we interpret the datum at once in Extensive 
Quantity, and derive the restricted Judgment as meaning that 
a part of the subject man is part of the class rational animal. 
But we should with equal legitimacy be able to restrict the 
predicate also. We can do this, however, under our ordinary 
use of language, only as we rather force the interpretation by 
viewing the proposition in its Comprehensive Quantity ; then 
the difficulty vanishes. Thus, if we explicate it, the notion 
man contains in it, as one of its component characters, that 
of rational, this being one of the complement of attributes 
rational animal ; we recognize the validity of the process. 
We then reason : The notion man contains the composite 
attribute rational animal; therefore, it contains the attri- 
bute rational. In like manner : Man is rational ; therefore, 
he is intelligent 

It will be observed that if another judgment be required 
in order to show that the new predicate is a part of the pred- 
icate in the sumption, the mediate reasoning or the syllogism 
will be called forth. 

§ 116. In Modal Restriction, the one condition of perfect 
Subjective thought is, that the restriction follow the order of 
lidaaf logical descent from the Apodictic to the Assertory 

Restriction. and Problematic ; from the Assertory to the Prob- 



METHODOLOGY OF REASONINGS. 189 

lematic. If the modal restriction be carried further into 
lower degrees of the Contingent, as may be done by means 
of the adverbs of modality, then the law requires that the re- 
striction be from the higher to the lower, and never the re- 
verse. Thus from necessarily true we may infer to the 
actually true, or to the probably true or possibly true, not con- 
versely. 

§ 117. In Immediate Seasonings by Transference, there 
are two distinct kinds — one consisting in the transference 
of Quality, the other in the transference of Modality from 
the copula of the Judgment to the terms. It was shown in 
the former Part, § 63, that in order to preserve the integrity 
and purity of the Thought, it is necessary to keep the trans- 
ference within the strict lines of Thought ; that is, since 
Thought can recognize only the relations of Whole and 
Part in its object-matter, all legitimate transference must be 
within the limits of those relations. In Transference of 
Quality, accordingly, the condition of perfect thought is, that 
the terms must be recognized as under the same Whole. 
Thus, in the proposition A is not B, in order to transfer the 
negation from the copula to the predicate, so as to infer A is 
non-B, A and B must be recognized as being in the same 
Whole. From the proposition : The scorpion is not verte- 
brate, we may legitimately infer the proposition, The scor- 
pion is invertebrate, only as we can recognize the term scor- 
pion as belonging to the Whole animal of which vertebrate 
and invertebrate are complementary parts. 

In the other kind of Transference, that by transfer of 
Modality, as, A is possibly B, therefore, A is a possible B, 
there is need of the same caution not to slip a quality of 
the thought surreptitiously over to the matter. If in the de- 
rived proposition, possible be interpreted as pertaining still to 
the copula, as it may be, there is, of course, no proper logical, 
but only a verbal, transference. But if it be taken as limit- 
ing the term B, then it can be a legitimate process of thought 
only, as in the case of Transference of Quality, when the 



190 PURE LOGIC. 

term as before transfer and the term as after transfer are com- 
plementary parts of a whole of which the other term must 
be a lower part. Thus we cannot from the proposition 
Sponge may be animal, that is, Sponge is possibly animal, 
infer Sponge is possible animal, that is, has all the charac- 
ters which make up the concept animal, and only lacks the 
character real. But from the proposition Sponge may be an 
animal, we may infer Sponge is a possible animal, having 
recognized it as possessing the essential character of an ani- 
mal — to wit: an alimentary cavity. 

§ 118. Of derivations of Judgments by Disjunction and 
TO . .. by Composition, it is unnecessary to add to 
and Compo- what has been, in the First Part, §§ 64, 65, indi- 
cated as constituting the essential conditions of the 
two processes. 

§ 119. In the Categorical Deductive Syllogism, the sub- 
jective conditions of perfect thought are : 

1°. That there be three and only three terms bearing the 
relation to each other of Major, Middle, and Minor ; the 
Middle being contained in or under the Major, and containing 
the Minor. 

2°. That the Sumption affirm or deny the Major to con- 
tain the Middle term, and the Subsumption affirm the Middle 
to contain the Minor term. 

3°. That the Conclusion affirm or deny the Major to con- 
tain the Minor term, according as the Sumption affirms or 
denies. 

4°. That the Thought in the Conclusion be not illegiti- 
mately changed to a higher modality than in the Antecedent. 

The first part of this Law requires that the Middle Term 
be recognized as standing in the relation of containing Whole, 
and contained part in the same kind of Whole, to the Major 
and Minor terms respectively. Violations of this Law in- 
volve the following fallacies : — 

The fallacy of using the word expressing the middle term 
in two different senses in the two premises. This fallacy is 



METHODOLOGY OF REASONINGS. 191 

called the Logical Quadruped, as it really introduces four 
terms instead of three into the Reasoning, and thus makes it 
go, as it were, on four feet. If the term is expressed by a 
single word, the fallacy is called simply an Equivocation ; if 
in a phrase, it is called an Amphibology. The following are 
examples : Mus est syllaba ; mus caseum rodit ; ergo, syllaba 
caseum rodit. 

Herod is a fox; a fox is a quadruped; therefore, Herod is 
a quadruped. 

Air is ponderable ; spirit is air ; therefore, spirit is pon- 
derable. 

You should eat what is sold in the market ; raw meat is 
sold in the market ; therefore, you should eat raw meat. 

Seven and two are odd and even numbers ; nine is seven 
and two ; therefore, nine is odd and even. This last is an 
example of what is called the Fallacy of Composition and 
Division, in which the middle term is used in one premise 
in its composite sense, in the other, in its distributive. 

The king can do no wrong ; Herod was king ; therefore, he 
was innocent. This is an example of the Fallacy a dicto se- 
cundum quid ad dictum simpliciter, consisting in the use of a 
word employed in one relation in one premise, and in another 
relation or without relation in the other. 

To this class belongs also the Fallacy of Unreal Univer- 
sality, as, The Cretans are liars ; Epimenides is a Cretan ; 
therefore, Epimenides is a liar. The word expressing the 
middle term in the Subsumption denotes the whole class of 
Cretans ; in the Sumption, it denotes only a large part of the 
class. 

In these fallacies there is a term which stands in each 
of the premises expressed by the same word ; but as this 
word is used in two different meanings, we have really two 
terms ; consequently there is no mediation of the Judgment 
— no proper derivation, no true reasoning. 

The fallacy in probation called petitio principii, Begging 
the Question, also, is to be detected by this Law. It con- 



192 PURE LOGIC. 

sists in taking as one of the premises a proposition equally 
needing proof as the conclusion itself. It appears in divers 
forms. First, generally, when a premise is assumed which 
is as much denied by the party addressed as the proposition 
to be proved ; as, when it is attempted to prove the Divinity 
of Christ to a Mohammedan from the authority of the Bible 
which he rejects ; or the cause of the planetary motion to be 
an ethereal vortex. This is the petitio principii proper; but 
the name has been applied to fallacies generally which lie in 
an illicit premise. 

A second form of this fallacy, the petitio principii, is the 
Hysteron proteron, in which the truth of the antecedent is 
dependent upon the conclusion ; as, when Scriptural testi- 
mony is urged in favor of the Being of God ; Scriptural 
testimony being valid only as it is the testimony of God, and 
therefore presupposing his existence. 

A third form of the petitio principii, is the Circle, in 
which the conclusion is disguised in one of the premises ; as, 
Lead falls to the ground quicker than feathers, because it is 
heavier. 

This vice is just the reverse of that in the Logical Quad- 
ruped ; as here the same meaning is conveyed in different 
language, so that there appear to be two distinct proposi- 
tions, while really there is but one. In the Logical Quadru- 
ped, on the other hand, two different meanings are hidden 
under the same guise of words. Dr. Whately has well ob- 
served that the English language peculiarly favors this fal- 
lacy, as we may express the same thought in Saxon or in 
Norman words ; thus : " To allow every man unbounded free- 
dom of speech must be best for the State ; for it is highly 
conducive to the interests of the community that each indi- 
vidual should possess unlimited liberty of expressing his 
sentiments." 

Still another fallacy in probation is the Saltus, in which 
one of the premises is neither expressed nor necessarily im- 
plied. This fallacy is practicable only by reason of the cir- 



METHODOLOGY OF REASONINGS. 193 

cunistance that the Enthymeme is ordinarily admitted in 
place of the fall reasoning. To verify an Enthymeme, it 
becomes necessary to supply the suppressed premise, when 
this vice in the thought at once shows itself. 

Further, it is implied in the rule that the terms be signif- 
icant, - — contain veritable thought. If, therefore, in the course 
of the reasoning, a term become insignificant, be a zero in 
thought, the reasoning is fallacious. This is exemplified in 
the familiar Algebraic demonstration that 7 = 23. For put- 
ting x=7 and y = 23, then as x -\- y = x -J- y, and so ax -(- 
ay = ax -|~ ay, and by transposition ax — ax = ay — ay, we 
have, by dividing by a — a, x = y or 7 = 23. 

Fallacies under the second part of the Law are liable to 
occur when it is not clearly distinguished which is the sump- 
tion and which the subsumption, so that the middle and minor 
terms are really differenced, instead of the major and middle ; 
in other words, the subsumption is of negative quality. Thus, 
Men are mortal ; angels are not men ; therefore, angels are 
not mortal ; or, Men are mortal ; brutes are not men ; there- 
fore, brutes are not mortal. 

Fallacies under the third part of the Law are such as fol- 
lows : Wise and good men were condemned by the Athenian 
populace ; Socrates was condemned by the Athenian populace ; 
therefore, he was a wise and good man. Here the conclu- 
sion has for its terms the minor and the middle. There is 
really no subsumption in this example, as the middle and the 
minor terms are compared only in the conclusion. 

Here belongs also the famous Fallacy, called Ignava Ratio, 
or Lazy Reason ; also the Reaper, the Controlling Reason, 
the Argumentum de Fato. Cicero thus states it : If it be 
fated that you recover from your present disease, whether you 
call in a doctor or not, you will recover ; again, If it be fated 
that you do not recover from your present disease, whether you 
call in a doctor or not, you will not recover : but one or other 
of the contradictories is fated ; therefore, to call in a doctor 
is of no consequence. 
13 



194 PURE LOGIC. 

Although it appears here in the form of a Hypothetico- 
Disjunctive Syllogism, and thus appears more plausible and 
difficult to detect, it is easily reducible to a Categorical De- 
ductive, thus : What is fated is unavoidable by any exertion ; 
the alternative of recovery from this sickness or death is fated ; 
therefore, the issue alike whether recovery or death is unavoid- 
able by any exertion. The sophism thus reduced is a pal- 
pable amphibology ; the conclusion has not the same term as 
minor that is contained in the subsumption ; — in the latter 
proposition it is an alternative of which something is predi- 
cated, while in the conclusion it is of the two factors of 
the alternative taken separately of which the predication is 
made. The only valid conclusion is : The alternative of re- 
covery or death is unavoidable by any exertion ; which is a 
very different proposition from this : This alternative, whether 
the one or the other — whether recovery or death — occur, is 
beyond the power of exertion to determine. 

By the application of this part of the Law, further, we 
may expose most of the diverse fallacies in probation classed 
under the generic name of mutatio elenchi, in the sense of 
change of the issue. The conclusion being the proposition 
which was originally in doubt and was to be proved, if the 
terms are not the same as in the original doubt a fallacy 
arises. Thus, if a person should undertake to prove the 
existence of ghosts, and should only prove some unusual 
noises and appearances during the night, he would exemplify 
this kind of fallacy. 

The violation of the fourth part of the Law may occur in 
two different forms, the first when a necessary Judgment 
is derived from an assertory or problematic, or an assertory 
from a problematic ; and the second, when the modality of 
the thought is covertly transferred to the matter. 

The first form may be exemplified thus: It rains when 
the moon changes ; the moon changes to-morrow ; therefore, it 
must rain to morrow. 

Of the second the following is an example : For aught we 



METHODOLOGY OF REASONINGS. 195 

know the deaf may be sensible of sounds within the ordinary 
hearing distance ; the deaf mute, Laura Bridgman, was 
within that distance when her teacher spoke to her ; therefore, 
Laura could have heard the direction of her teacher. 

The common Fallacy of Non causa pro causa, or Post hoc, 
ergo propter hoc, in which only general antecedence is ac- 
cepted as universal, or a causal connection is inferred from 
such general antecedence, belongs under this species. This 
variety of fallacy is extremely common ; but like popular 
reasonings it is generally in the form of an Enthymeme, the 
sumption being suppressed. Thus : The moon will change 
to-morrow ; therefore, it must rain to-morrow. 

§ 120. In the Categorical Inductive Syllogism, the sub- 
jective conditions of perfect thought are : 

1°. That there be three and only three terms, two of 
which bear the relation to each other of Part and Comple- 
mentary Part, and the third bears the relation of Whole 
alike to each of these tw r o. 

2°. That the Sumption affirm or deny this third of one of 
the other two, and the Subsumption affirm these two to be 
Complementary of each other. 

3°. That the Conclusion affirm or deny the third of that 
term of which it is not predicated in the Sumption. 

4°. That the Modality be not illegitimately changed. 

Of the application of this general Law of the Inductive 
Syllogism, it will be unnecessary to speak in detail, except 
in respect to the one feature in which it differs from the De- 
ductive. This peculiar element in the Law is in the second 
part which requires that the Subsumption affirm two of the 
terms to be complementary of each other, and the main dif- 
ficulty is in the objective bearings of the rule, in verifying 
this premise as a true judgment. As in Deductive Reason- 
ing, so in Inductive and to a much greater extent, a part of 
the Antecedent is usually suppressed in discourse ; and inas- 
much as logical literature has confined itself mainly to the 
former, we are less familiarized with the process of supplying 



196 PURE LOGIC. 

the suppressed part in Induction in order to verify the rea- 
soning. There is still another difficulty arising from the 
fact that this reasoning more commonly proceeds in Causal 
Wholes with which logical systems have concerned them- 
selves as little as with Induction, and with the movements 
of Thought generally in the relation of Part and Comple- 
mentary Part. 

As Logical Methodology aims to guide to true Science by 
unfolding the conditions of perfect thought, both material 
and formal, and as all proper thought is under the general 
relationship of Whole and Part, including, of course, that of 
Part and Complementary Part, we shall more intelligently 
and securely reach the conditions of a true Induction by 
illustrating the process in its application to the several kinds 
of quantity separately. 

And, first, in proper logical wholes — the wholes of Exr 
tension and Comprehension. These wholes, we have seen, 
are the pure products of thought. We have seen how they 
are produced; how concepts are formed by a synthesis of 
the homologous terms of two or more judgments having the 
same analogous term, which we have called the Base of the 
concept. We have seen how concepts, thus springing into 
existence in the progress of human intelligence, at once em- 
body themselves in words. We have seen how by two 
movements in opposite directions but perhaps synchronous, 
according as the subject or the predicate of the primitive 
judgments is taken as the Base, the concept and its embodi- 
ment — the word becomes narrowed or extended, whether by 
occasion of the more extended observation of its matter, and 
the consequent rectification of its objective import, or of the 
needs of thought for fuller or more discriminating symbols. 
Now these concepts so formed and modified, and these words, 
their verbal embodiments, may become matter of thought — 
matter of inductive thought. They are accepted as its data. 
If they have been perfectly formed, then the inductive 
process begins with objective truth. So in fact it ordinarily 



METHODOLOGY OF REASONINGS. 197 

begins. It is obvious that just so much of contingency as 
attaches to the original data as thus furnished by the con- 
spiring and restless energies of all who use the language and 
formed the concept, must attach to the results of the induc- 
tion itself; and, so far as its material perfection is concerned, 
no more. 

We will now look at the subjective element — the induc- 
tive process itself — to see how far necessary certainty may 
attach to it, and how far this process may be relied on to ad- 
vance knowledge. It is apparent at once, from the very 
nature of a concept, then, that the Base of the concept, and 
any part of the Base, must belong to "every part of the 
concept itself alike. If horse, ox, dog, are parts of the con- 
cept quadruped, then the Base on which the concept was 
formed, four-footed, and every part of four-footed, must be- 
long to each part alike, to horse, ox, dog. Now in Induction 
as applied to concept wholes, the problem is simply this : 
Given horse as four-footed for one premise, and given, also, 
ox, dog, as complementary part of horse, as the other part of 
the antecedent, and we induce with absolute certainty that 
ox, dog, are four-footed. This is but retracing the steps by 
which the concept was formed — the analysis of the original 
synthesis ; and if that was true, the result of the induction 
is also true. 

While unhesitating assent must be yielded to this repre- 
sentation of the validity of the inductive process, yet it may 
remain in doubt whether there be any advance made in any 
real knowledge, as we seem to have no more than we had 
when we formed the concept. But a brief reflection will 
convince us that induction in mere concepts — the pure prod- 
ucts of human thought, — gives to each of us a large share 
of all the knowledge we severally possess. Concepts, words, 
are not the product of one individual thought, but, so to 
speak, of the conspiring thought of the race. Each thinker 
has contributed to their formation and modification. How 
much, for instance, quadruped imports, has been determined 



198 PURE LOGIC. 

by this conspiring thought. If all that forming, shaping 
thought could be imagined to be garnered up in one body of 
living activity, preserving the entire complicated movement 
that shaped the concept, then to such an activity no advance 
of knowledge could, perhaps, be supposed to be effected by 
the analysis of the forming movement in induction. But 
the fact is that no individual thinker contributes more than 
the minutest fraction to the whole formation. To the indi- 
vidual, therefore, the analysis may bring all the knowledge 
that was possessed by all the contributors to the formation. 
But, farther, the work of forming concepts and concept- 
words is a silent, unintentional, and so far unconscious work, 
even on the part of their very framers. They are the spon- 
taneous, instinctive product of man as a social organism, as 
a thinking, and speaking yet cooperative nature. "The very 
creator of language can know his own product only as he 
can take to pieces again the wondrous complication. Induc- 
tion, thus, is the condition and chief means not only of indi- 
vidual progress in intelligence, but of that of the community, 
the race. Accordingly, a great part of the advance of 
knowledge on the part of individual learners consists in the 
resolution of concepts by a proper induction — by inducing 
the Base or parts of the Base from any given part to any 
proper complementary part. 

Not only this, but the sum of human knowledge is aug- 
mented more by Induction than by any other of the processes 
of thought, if it be possible to separate in such a comparison 
mutually dependent processes. This will appear at once 
from the consideration that while the enlargement of the 
Base of the concept may be effected by observation applied 
to any one part of it, every such enlargement enures to the 
spread of our knowledge over all the parts. Thus, in the 
concept quadruped, if an observer of nature discover in his 
inspection of an individual horse a previously unknown prop- 
erty or character belonging to it so far as quadruped, we 
will suppose some structure of a joint necessary to the mo- 



METHODOLOGY OF REASONINGS. 199 

tion of such an animal, before unnoticed, he not only induces 
from* the individual horse observed to every other horse, but 
to every other quadruped. Nor does the increase of knowl- 
edge originating in this single discovery stop here. But 
from this property other properties may be induced indefi- 
nitely, as to mode of locomotion, position, and numberless 
other relations of other parts of the animal structure, habits 
of life even, and utilities without end. 

Subjectively, then, Induction in concepts bears the charac- 
ter of absolute certainty. Objectively, it bears the charac- 
ter of contingency which attaches to the datum — the con- 
cept itself. This, however, as the legitimate product of 
mankind as speech-forming, is to be accepted as valid. 
Here more than anywhere else does the adage hold true — 
Vox populi, vox Dei ; — the conspiring thought of the race 
is the thought of truth. Even the skeptic accepts the con- 
cept as valid ; he could not advance a step in his argumenta- 
tion but as he is supported on the truth of concepts. More- 
over, Induction is not only a valid instrument of knowledge, 
it is a chief- instrument of knowledge to thinking, speaking 
man. And the simple condition of perfect thought which 
shall give us assured truth or perfect science is that we 
keep within the relationship of part to complementary part. 
This, however, is by no means difficult in case of concept 
wholes. The chief liability to fallacious reasoning lies in 
our not rightly apprehending the base of the concept. 

Induction in the wholes proper to the object-matter of 
thought, bears the same character of subjective certainty. 
That the part necessitates its complementary part is a neces- 
sary truth. 

Objectively, the validity of Induction in this kind of wholes 
depends on the truth of the data, first, that the given part is 
a part of the whole object thought ; secondly, that the other 
part is truly complementary. In an Integrate Whole, thus, 
if head be given as part of 7nan, and body be given as com- 
plementary part, then we may induce that whatever is true of 



200 PURE LOGIC. 

head as part of man — for instance, organic — is true of body ; 
while we induce the different of it as complementary ; thus, 
if head is higher, body is lower ; if head is guiding, body is 
guided, and the like. 

In a Substantial Whole, if bi-manous be given as part of 
man as physical, and mammal as complementary, then what- 
ever of physically human may be true of bi-manous as part, 
cellular, for instance, may be induced of mammal ; while, on 
the other hand, we may induce of it as complementary, the 
different ; as that, if bi-manous is prehensile, mammal is 
non-prehensile. In the same way if rational spirit be given 
to us as a substance having the attributes of intelligent, emo- 
tional, and voluntary, we may induce that whatever is true 
of intelligent simply as part of rational spirit is true of emo- 
tional and voluntary, as, for instance, that they are active, 
capable of growth, dependent on conditions, limited, and the 
like ; and also as complementary, that they are not cognitive, 
not reasoning, and the like. 

So in a Causal Whole, if the cause with one part of its 
effect be given, we may induce to the complementary effect 
the same and also the different. If, thus, solar heat be given 
as cause, and this piece of expanded iron be given as part 
effect, we may induce the same of every piece of iron within 
the sphere of the causal agency. So if there be given a 
causal agency in creating, which produces a flower with a 
definite number, order, figure, color of organs, and a definite 
fragrance, we induce the same of every other flower within 
the same causal sphere. The principle of Induction, that 
the part necessitates its complementary part, holds here as 
everywhere else. The peculiar difficulty here lies in ob- 
serving the objective law of induction — in verifying the 
data, determining the causal whole and the complementary 
parts. All the numerous rules prescribed in material Induc- 
tion so called, are comprehended in this one objective law of 
Induction — Verify the parts as complementary of each other 
in the same causal whole. This principle will determine 



METHODOLOGY OF REASONINGS. 201 

whether one observation or more are necessary. One obser- 
vation may in some cases be sufficient to ascertain the exist- 
ence of the cause, its sphere, its liability to be overborne by 
other causal agencies, or to be hindered by failing conditions, 
— may. in short, verify the data. In other cases more may 
be required ; and how many may be requisite must be deter- 
mined by the occasions of the induction or by the specific 
peculiarities of its object-matter. 

All this is, however, aside from the proper design of pure 
logic. It belongs to Applied Logic to prescribe the mode of 
ascertaining the causal sphere, to indicate the degree of 
contingency that attaches to the matter, the datum attained 
for the inductive process, and by what methods, if by any, 
that degree may be reduced to a minimum. It is impossible 
to eliminate all contingency ; for, as has been shown, the 
necessary lies exclusively in the realms of thought, and all 
that is foreign to thought must bear the character of contin- 
gent. But this contingency may be, for any particular use 
in our thinking, an infinitesimal ; and thought may accept 
the datum as not to be questioned. In fact, we do accept 
the reality of External Existence ; we accept the reality of 
Being, both as Substance having attributes, and as Cause pro- 
ducing effects ; we accept the diversity and the stability of 
things — that each thing, whether substance or cause, has its 
own permanent attributes, so that each substance will retain 
each essential property that it is now found to possess, for to- 
morrow and the next year, and each cause work its own proper 
effect here and elsewhere alike. The contingency that rises 
in all this we dismiss from our thought, and treat such matter 
as true beyond impeachment. But when we pass one step 
further, and endeavor to ascertain the real diversity of sub- 
stances with their several properties and of causes with their 
several effects, we come upon a contingency that may inval- 
idate our whole thought-process applied to it. We cannot 
induce that any one property which belongs to a given sub- 
stance to-day will be found to belong to it to-morrow, or be- 



202 PURE LOGIC. 

longs to a substance having all the other properties elsewhere, 
until we have discriminated it as an essential property, not 
an accidental one ; we cannot induce that any one effect 
which we find to-day proceeding from a given cause before 
us will be found proceeding from it to-morrow r , or from a 
cause working all the other effects, but working elsewhere. 
How to discriminate the essential from the accidental, it is 
the province of Applied Logic in each department of knowl- 
edge to indicate — to determine by what methods, and to what 
extent these methods must be carried that the contingency 
may be reduced to the requisite degree, and to prescribe the 
tests, and checks also, as well as the methods of observation. 
Such a science, both in its general principles and also in its 
bearing on each of the departments of knowledge, is a great 
desideratum, as well for the more rapid advancement of science 
as for its verification. Not a little will be gained, however, 
in the interest of human knowledge, if the thought-process 
be carefully discriminated from the matter to which it is ap- 
plied, and its nature and laws be well understood. And a 
further gain, by no means inconsiderable, will also be secured, 
if it is ascertained precisely what is to be done in construct- 
ing a methodology for any particular field of scientific induc- 
tion, in so far as regards the several conditions of perfect 
science. 

§ 121. In the Hypothetical Syllogism, the Law of perfect 
cognition requires — 

1°. That the premises, the terms of which are here Judg- 
ments, be recognized and verified, and particularly the mode 
of relation which is affirmed between the terms of the Sump- 
tion, whether that of Whole to Part, or of Part to Comple- 
mentary Part. 

2°. That the Conclusion affirm the consequent member of 
the Sumption in the Affirmative or Ponent form, and deny 
the antecedent member in the Negative or Tollent form of 
the Syllogism. 

The difficulty in respect to the first or objective condition 



METHODOLOGY OF REASONINGS. 203 

of a valid Hypothetical Reasoning is twofold : that of sup- 
plying the part of the antecedent which is suppressed ; and 
that of distinguishing, in order to verification, the character 
of the Sumption, whether it expresses the relation of Whole 
to Part, or of Part to Complementary Part. Either premise 
may be suppressed, and in either relation of the terms of the 
Sumption. Thus we may reason, either: If the sun had 
arisen, it must have been light ; therefore, the sun could not 
have arisen, suppressing the subsumption ; or, The sun had 
arisen ; therefore, it was light, suppressing the sumption. 
We may also reason : If virtue is voluntary, vice is volun- 
tary ; therefore, vice is voluntary, suppressing the subsump- 
tion, but virtue is voluntary ; or, Virtue is voluntary ; there- 
fore, vice is voluntary, suppressing the sumption. 

One of the chief liabilities to error in the subjective ele- 
ment of the reasoning arises in the negative form, when the 
antecedent member of the sumption is also negative, from 
the doubling of negatives ; as, If vice be not voluntary, virtue 
must be necessitated ; but virtue is not necessitated; there- 
fore, vice is not voluntary. Here the fallacy is obvious ; but 
it may be covered up and especially in a chain of reasoning, 
in extended phrases, so as to escape ready detection. 

§ 122. In the Disjunctive Syllogism, the Law of perfect 
thought requires — 

1°. That the disjunction in the Sumption be verified, and 
if it be in the terms or in contrary opposition by reduction 
to strictly logical contradiction. 

2°. That the Conclusion always be in quality opposed to 
the Subsumption, and have for its predicate the disjunct 
member not subsumed. 

In application of this principle of method, the chief dif- 
ficulty will lie in reducing the opposition to strict logical 
contradiction. The most fallacious form of this reasoning 
is, perhaps, where there is true opposition, but it lies in 
the terms, the matter, not in the thought ; as, A is B or 
non-B. But it is unnecessary to add here to what has been 



204 PURE LOGIC. 

already said of this distinction, which has been overlooked 
even by logicians generally. 

§ 123. In the Hypothetico-Disjunctive Syllogism or the 
Dilemma, the Law of perfect thought requires - — 

1°. That the antecedent be verified, in respect both to the 
disjunction and the hypothetical judgment in the Sumption, 
and, also, in respect to the positing or the sublation in the 
Subsumption. 

2°. That the Conclusion sublate the antecedent member of 
the Sumption, or posit the Consequent, and not conversely. 

A fallacy in this process of reasoning has become quite 
famous. There are two accounts, the Greek and the Roman. 
" The Roman account is given us by Aulus Gellius, and is 
there told in relation to an action between Protagoras, the 
prince of the Sophists, and Euathlus, a young man, his dis- 
ciple. The disciple had covenanted to give his master a 
large sum to accomplish him as a legal rhetorician ; the one 
half of the sum was paid down, and the other was to be paid 
on the day when Euathlus should plead and gain his first 
cause. But when the scholar, after the due course of pre- 
paratory instruction, was not in the same hurry to commence 
pleader as the master to obtain the remainder of his fee, 
Protagoras brought Euathlus into court, and addressed his 
opponent in the following reasoning : ' Learn, most foolish of 
young men, that however matters may turn up — whether the 
decision to-day be in your favor or against you — pay me my 
demand you must. For if the judgment be against you, I 
shall obtain the fee by decree of the court ; and if in your 
favor, I shall obtain it in terms of the compact, by which it 
became due on the very day you gained your first cause. 
You thus must fail, either by judgment or by stipulation.' To 
this Euathlus rejoined : ' Most sapient of masters, learn from 
your own argument, that whatever may be the finding of the 
court, absolved I must be from any claim by you. For if 
the decision be favorable, I pay nothing by the sentence of 
the judges ; but if unfavorable, I pay nothing in virtue of the 



METHODOLOGY OF REASONINGS. 205 

compact, because, though pleading, I shall not have gained 
my cause. The judges, says Gelli us, unable to find a ratio 
decidendi, adjourned the case to an indefinite day, and ulti- 
mately left it undetermined. A parallel story is told, among 
the Greek writers, of the rhetorician Cprax, anglice Crow, 
and his scholar Tisias. In this case, the judges got off by 
delivering a joke against both parties, instead of a decision 
in favor of either. We have here, they said, the plaguy 
egg of a plaguy crow ; and from this circumstance is said 
to have originated the Greek proverb, kclkov KopaKos kolkqv 

<x)OV, 

The fallacy in the reasoning of Protagoras lies in the am- 
biguity of the second member of his disjunction, that if 
Euathlus won the suit, the money would be due by the terms 
of the compact ; it would become due only after the decision, 
and by virtue of it. The fallacy in the reply of Euathlus, 
lies also in a similar ambiguity in the second member of his 
disjunction, that the decision of the court reached to a claim 
that would arise only on the event of that decision. Before 
the decision Protagoras had no claim, and of course must lose 
his suit ; on losing his suit, his claim emerged to full valid- 
ity, and after that could be enforced. In both reasonings 
there is thus the fallacy of substituting in the conclusion a 
different claim from that which is presented equivocally in 
the antecedent : in the one, a claim before the decision of 
the case, in the other a claim coming to be only after the 
decision. 

§ 124. In the Poly syllogism, whether Epichirema or So- 
rites, we have only to verify the several links of the chain, 
both objectively and subjectively, as in any case of composite 
reasoning, at the same time attending to the consecution of 
the thought that that be ever legitimate. In categorical 
reasonings the attention will be chiefly directed to the middle 
term, to see that there be a true middle in every separate 
link of the chain ; and to the carrying forward of the same 
judgment from the place of conclusion in one link to that of 



206 PURE LOGIC. 

antecedent in the next. In conditional reasonings, in like 
manner, the attention should be chiefly directed to the medi- 
ating judgments, and then to the carrying forward of the con- 
clusions in the several links. 



PURE LOGIC. 

PART III. 

LOGICAL PEAXIS. 



CHAPTER I. 

I. EXERCISES IN JUDGMENTS. 

Exercise 1. Judgments to be severally discriminated as 
to — 

1. Quality: whether Affirmative, Negative, or Disjunct- 
ive ; 

2. Modality : whether Assertory, Problematical, or Neces- 
sary ; 

3. Degree of Identity : whether Total or Partial ; 

4. Nature of Terms : whether Categorical or Hypothetical ; 

5. Logical Quantity : whether Comprehensive or Exten- 
sive; 

6. Nature of Whole: whether Integrate, Substantial, or 
Causal ; and the parts of the Sentence respectively contain- 
ing the Terms and the Copula to be indicated. 

Models. — The Judgment Man is mortal, is Affirmative, Assert- 
ory, Partial, Categorical, Comprehensive, Substantial ; the Judg- 
ment, Alexander may not have practiced what he had learned of his teach- 
er, is Negative, Problematical, Partial, Categorical, Comprehensive, 
Causal. The Judgment, If Alexander had been a consistent disciple of 
Aristotle, he would have rxded his appetites, is an Affirmative, Assertory, 
Partial, Hypothetical, Comprehensive, Causal Judgment. If Alex- 
ander had ruled his ambition, he would either have made no conquests or 



208 PUKE LOGIC. 

have maintained them, is a Disjunctive, Assertory, Partial, Hypotheti- 
cal, Comprehensive, Causal Judgment. 

1. Iron is magnetic. 

2. Iron is not soluble in water. 

3. Tron either is magnetic or is not magnetic. 

4. Iron must be magnetic. 

5. If iron be magnetic, it has polarity. 

6. Iron is a metal. 

7. Iron nourishes plants. 

8. Steel is carbonized iron. 

9. Thought is a cognition. 

10. Thought is a relative cognition. 

11. Thought either is a mediate cognition or is an imme- 
diate cognition. 

12. If thought is a mediate cognition, it is beyond its 
province to account for its object. 

13. Logic is the science of necessary thought. 

14. Logic methodizes knowledge. 

15. Logic contains the doctrine of elements and the doc- 
trine of method. 

16. If logic is the doctrine of thought, it is the necessary 
guide to all intelligent and certain thinking. 

17. Thought does not amplify the matter of knowledge. 

18. Thought either creates all truth or creates no truth. 

19. Truth is knowledge of things as existing. 

20. The knowledge of things as existing is relative cog- 
nition. 

21. The elements of thought are judgments, concepts, and 
reasonings. 

22. A cognition is either relative or irrelative. 

Exercise 2. Disjunctives in Contrary Opposition to be 
reduced to Contradictory Opposition. 

Model. —Angles are right or not right; as not right they are 
acute or not acute, that is, obtuse. 

1. Angles are right, acute, or obtuse. 



EXERCISES IN JUDGMENTS. 209 

2. Triangles are equilateral, isosceles, or scalene. 

3. A quadrilateral figure is either a square, an oblong, a 
rhombus, a rhomboid, or a trapezium. 

4. Bodies are in stable, in unstable, or in indifferent equi- 
librium. 

5. A body will be supported if the point of support be 
applied at, below, or above the center of gravity. 

6. A body is at rest, in relative motion, or in absolute 
motion. 

7. Motion is either horizontal, perpendicular, inclined, or 
rotary. 

8. Winds are constant, periodical, or variable. 

9. Mirrors are plane, convex, or concave. 

10. The kingdoms of nature are the mineral, the vegeta- 
ble, and the animal kingdom. 

11. A carnivorous animal either walks on the sole as man, 
on the toes as the dog, or is amphibious as the seal. 

12. A ruminant animal is either horned like the ox, or a 
camel or a llama. 

13. The thick-skinned order of animals either have trunks 
like the elephant, or have no trunks like the swine, or are 
single-hoofed like the horse. 

14. He is either standing, or sitting, or lying. 

15. The color is blue, or yellow, or red. 

16. Attention is either purely spontaneous, prompted by 
desire, or voluntary. 

17. Space is finite, infinite, or ideal. 

18. A judgment is either affirmative, or negative, or dis- 
junctive. 

19. The world is either eternal, or the result of chance, 
or the work of an intelligent Creator. 

20. The virtues are either passions, faculties, or habits. 

21. The languages are either monosyllabic, agglutinative, 
or inflectional. 

Exercise 3. (1.) Judgments, the Modality of which is to 
14 



210 PURE LOGIC. 

be changed ; as from Problematic to Assertory and Apodictic, 
and the reverse. 

1. It may rain to-morrow. 

2. It is possible that Eneke's comet will appear again in 
three and a third years. 

3. There may have been such a character as the Wander- 
ing Jew. 

4. Such a rain must have been accompanied by atmos- 
pheric movements of great violence. 

5. Judicious exercise must invigorate. 

6. No man can know that he reasons soundly who does 
not know something of the laws of thought. 

7. No possible benefit can result. 

8. Alexander possibly conquered Darius. 

9. Integrity will certainly reap its reward. 

10. Two wrongs cannot make one right. 

(2.) Propositions, the Modality in which is to be discrimi- 
nated, whether in the Copula or the Terms ; or if equivocal, 
the ambiguity to be removed. 

1. He is a possible witness. 

2. No merely probable issue will justify the adventure. 

3. A relapse is possible. 

4. The relation between cause and effect is a necessary 
relation. 

5. He must go ; the command is peremptory. 

6. No possible good can result. 

7. Perhaps he will succeed. 

8. It necessarily comes about that we are here to-day. 

9. Altogether unnecessary is all this display. 

10. Life must end soon. 

Exercise 4. Partial Judgments to be explicated so as to 
show the Parts of the Terms which are identified. 

Model. — One of the characters that make up the concept, man, 
is identical with mortal ; man is one of the parts that make up the 
class biped. 



EXERCISES IN JUDGMENTS. 211 

1. Man is mortal. 

2. Man is a mortal. 

3. Man is two-footed. 

4. Man is a biped. 

5. Bucephalus is one-hoofed. 

6. Bucephalus is a quadruped. 

7. A judgment is a product of thought. 

8. A judgment is an act of thought. 

9. A judgment is thought. 

10. The judgment is correct. 

11. The judgment is partial. 

12. The proposition is complex. 

13. The proposition is true. 

14. Virtue is voluntary. 

15. Veracity is a virtue. 

16. Veracity is voluntary. 

17. Whatever is moral is voluntary. 

18. Every voluntary act is moral. 

Exercise 5. Hypothetical Judgments to he explicated. 

Models. — In the Hypothetical, If I think I am, the Judgment 
that / think involves the Judgment that 1 am, as action is part of being 
as cause. In the Hypothetical, If virtue is voluntary, vice is voluntary, 
the Judgment that virtue is voluntary involves the Judgment that 
vice is voluntary, as virtue is the complementary part of vice. 

1. If one dozen dozen are twelve dozen, half a dozen 
dozen are six dozen. 

2. If one acre contains one hundred and sixty square rods, 
one fourth of an acre contains forty .rods. 

3. If the world were eternal, there would be records prior 
to the Mosaic. 

4. If the English are Anglo-Saxons, they are Caucasians. 

5. If I think, I am. 

6. If the universe exhibit design, it is the work of intel- 
ligence. 

7. If a digestive cavity marks an animal, the polyp is an 
animal. 



212 PURE LOGIC. 

8. If matter is entirely inert, there is a higher moving 
power. 

9. If we cannot help an evil, we should not fret about it. 

10. If we can help an evil, we should not fret about it. 

Exercise 6. Judgments to be explicated in Comprehensive 
and also in Extensive Quantity. 

1. Man is rational. 

2. Glass is brittle. 

3. Gold is ductile. 

4. Thought is spiritual. 

5. Passion is catching. 

6. Ignorance is degrading. 

7. To lie is cowardly. 

8. To be ungrateful is base. 

9. To die is to sleep. 

10. To be an Athenian is to dare. 

11. That we still breathe is of mercy. 

12. That God reigns is truth of richest comfort. 

13. Wisdom is no inheritance. 

Exercise 7. Judgments in Integrate, Substantial, and 
Causal Wholes to be discriminated, explicated, and, when 
necessary, corrected, 

1. The surface of a square is double that of a triangle 
on the same base and of the same height. 

2. A whole is equal to the sum of its parts. 

3. A square is equal to the sum of the squares of any two 
parts into which it may be divided, together with double the 
rectangle of its parts. 

4. A whole contains each of its parts. 

5. The solar system contains the sun, planets, and their 
satellites. 

6. The body consists of solids and fluids. 

7. Atmospheric air is composed of oxygen and nitrogen. 

8. Water consists of oxygen and hydrogen. 



EXERCISES IN JUDGMENTS. 213 

9. Percussion is a combination of friction and compression. 

10. A square is rectangular. 

11. The sun is luminous. 

12. The atmosphere has weight. 

13. Europe is temperate. 

14. Fire burns. 

15. The wood burns. 

1 6. The bellman rings. 

17. The bell rings. 

18. The sun illuminates the earth. 

19. The earth reflects the light of the sun. 

20. Vulgar eyes judge rather by the event than by the 
intention. 

21. Fortunate is better than wise. 

22. The mind's excellency can solve the real blemishes of 
the body. 

Exercise 8. Propositions to be corrected, with indication 
of the particular imperfection, whether in respect of Matter ', 
of Judgment, or of Expression. 

1. Triangles are either equilateral or equi-angular. 

2. Triangles are right-angled, isosceles, or scalene. 

3. All that glitters is not gold. 

4. The gods of the heathen are no gods. 

5. No God is worshiped there. 

6. Not all the ills of earth can mar my joy. 

7. Some prudence is commendable. 

8. We do not admit a possible failure into our plans. 

9. A bold front must win for us. 

10. Animal body is composed of flesh, bones, and muscles. 

11. The atmospheric air is made up of oxygen, nitrogen, 
carbonic acid, and electricity. 

12. Root, trunk, bark, and branches form the tree. 

13. Embryos in pines are radicles or stemlets. 

14. Every chemical substance has combining or equivalent 
members. 



214 PUEE LOGIC. 

15. Simple bodies are divided into two classes, metals and 
metalloids, or non-metallic elements. 

16. Leaves are opposite or alternate. 

17. The eastern winds here are winds that blow from the 
tropics or trades. 

18. Oxygen forms with silicon silica or silicic acid. 

19. Of spiry or spire-shaped trees, the firs or spruces are 
the best illustrations. 

II. EXERCISES IN CONCEPTS. 

Exercise 9. Concepts to be defined ; to be analyzed, also, 
both by Division and Partition. 

1. Animal. 2. The Lynx. 3. The Beaver. 4. The 
Armadillo. 5. The Zebra. 6. The Dromedary. 7. The 
Reindeer. 8. The Antelope. 9. The Dolphin. 10. The 
Eagle. 11. The Thrush. 12. The Linnet. 13. The Spar- 
row. 14. The Jay. 15. The Hoopoe. 16. The Lapwing. 
17. The Flamingo. 18. The Pelican. 19. The Teal. 20. 
The Basilisk. 21. The Chameleon. 22. The Cobra Ca- 
pello. 23. The Salamander. 24. The Flying-Fish. 25. 
The Torpedo. 26. The Argonaut. 27. The Lobster. 28. 
The Tarantula. 29. The Cochineal. 30. The Thistle Bird. 
31. The Violet. 32. The Pomegranate. 33. The Cypress. 
34. The Amethyst. 35. The Emerald. 36. Topaz. 37. 
Heat. 38. Crystal. 39. Carbon. 40. Mercury. 41. Oxyd. 
42. Monsoon. 43. Botany. 44. Grammar. 45. Psychology. 
46. Intellect. 47. Virtue. 48. Hope. 49. Purpose. 50. 
Habit. 51. State. 52. Church. 53. Government. 54. 
Money. 55. Art. 56. Industry. 57. Agriculture. 58. 
Ship. 59. Navy. 60. Judiciary. 

in. exercises in reasonings. 

Observation. — As the movements of Thought in ordinary dis- 
course are abbreviated and complicated, it is necessary, in order to 
verify them, to reduce them to their full logical form in their several 
distinct elements. In order to this, it will be found convenient to 
separate the Terms, and mark them by familiar signs, as W, P, and 



EXERCISES IN REASONINGS. 215 

My for Major, Minor, and Middle Terms, respectively, and to place 
the Judgments in a fixed order, the antecedent with its Sumption 
and Subsumption, if it be a Mediate Reasoning, above, and the con- 
sequent below. Begin with the conclusion ; mark the Terms as W 
and P respectively ; then find the Middle Term or Terms, and con- 
struct the Sumption and the Subsumption. The reasoning will then 
be readily recognized as valid or not by the application of the Rules 
of Reasoning. 

Exercise 10. Complex Reasonings to be resolved. 

1. All poets are men of genius; therefore, some men of 
genius are poets. 

2. He who is content with what he has, is truly rich ; a 
covetous man is not content with what he has ; therefore, no 
covetous man is truly rich. 

3. All the righteous are happy ; therefore, all who are 
unhappy are unrighteous. 

4. All insincere men are dishonest ; therefore, all honest 
men are sincere. 

Exercise 11. Reasonings with suppressed Premises to be 
supplied. 

1. All tyrants deserve death ; therefore, Caesar deserved 
death. 

2. Whatever comes from God is entitled to reverence ; 
therefore, the Scriptures are entitled to reverence. 

3. Of two evils, the less is to be preferred ; occasional 
turbulence, therefore, is to be preferred to rigid despotism. 

4. Wine is hurtful ; for all stimulants are hurtful. 

5. An infant has no moral power; therefore, it has no 
responsibility. 

6. Kings have no friends ; for they have no equals. 

7. The lion is a predaceous animal ; therefore, it is not 
ruminant. 

8. Innate ideas cannot be enumerated ; therefore, they do 
not exist. 

9. Solon was a wise legislator ; for he suited his laws to 
the genius of his nation. 



216 PURE LOGIC. 

10. The Epicureans cannot be regarded as true philoso- 
phers ; for they did not reckon virtue a good in itself. 

11. Shame is not a virtue ; for it is more a passion than a 
habit. 

12. Gambling implies a desire to gain by another's loss; 
therefore, it is a violation of the tenth commandment. 

13. Onesimus was a servant of Philemon ; Philemon was 
a hearer of Archippus ; Archippus was a minister at Colosse ; 
therefore, Onesimus was a resident at Colosse. 

14. The nervous fluid is not electricity ; for electricity 
may be transmitted along a nervous trunk which has been 
compressed by a string tied tightly round it, whilst the pas- 
sage of ordinary nervous power is as completely checked by 
this process as if the nerve had been divided. 

Exercise 12. Reasonings to be discriminated as to their 
nature, as Immediate, Categorical, or Conditional, with indi- 
cation of Mediating Judgments in the latter, and Middle 
Terms in Categorical Syllogisms. 

1. Equilaferal triangles are equi-angular ; therefore, equi- 
angular triangles are equilateral. 

2. Government is either a property or a trust ; it is not 
a property ; it must, therefore, be a trust. 

3. If there were no divine Providence, no human govern- 
ment could long subsist ; various human governments have 
subsisted long; therefore, there must be a divine Provi- 
dence. 

4. The early and general assignment of the Epistle to the 
Hebrews to the Apostle Paul as its author, must have been 
either from its professing to be his, or from its really being 
his ; but it does not profess to be his ; therefore, it is really 
his. 

5. No person can serve God and mammon ; the covetous 
man serves mammon ; he cannot, therefore, serve God. 

6. If the prophecies of the Old Testament had been written 
without knowledge of the events of the time of Christ, they 



EXERCISES IN REASONINGS. 217 

could not have corresponded with them exactly ; and if they 
had been forged by Christians, they would not be preserved 
and acknowledged by the Jews : but they did correspond 
with those events, and they are preserved and acknowledged 
by the Jews ; therefore, they were neither written without 
knowledge of those events, nor were they forged by Chris- 
tians. 

7. The favor of God must be bestowed either with respect to 
men's persons or with respect to their conduct ; but " God is 
no respecter of persons ; " therefore, his favor must be be- 
stowed with respect to men's conduct. 

8. If any complete theory could be framed to explain the 
establishment of Christianity by human causes, such a theory 
would have been proposed before now ; but no such theory 
ever has been prepared ; therefore, none can be framed. 

9. If the system of the universe is not the best possible, we 
must suppose either that the Creator did not prefer a better 
one, or that he knew no better one, or that he could not 
create a better ; but we can entertain neither of these sup- 
positions, for we should thereby limit his goodness, his intel- 
ligence, or his power ; therefore, the system of the universe 
is the best. 

Exercise 13. Fallacies to be detected. 

"By discourse," says Chillingworth, meaning by the word the 
operation of the discursive faculty, or Thought, " no man can possibly 
be led into error; but if he err in his conclusions, he must of neces- 
sity either err in his principles or commit some error in his discourse ; 
that is, indeed, not discourse but seem to do so." 

1. All men are mortal ; therefore, all mortals are men. 

2. No man is infallible ; therefore, every fallible being is 
human. 

3. All men are not virtuous ; therefore, all men are 
vicious. 

4. All unjust acts should be punished ; therefore, all acts 
not punished should be just. 



218 PURE LOGIC. 

5. No evil should be allowed that good may come of it ; 
all punishment is an evil ; therefore, no punishment should 
be allowed that good may come of it. 

6. A problem is neither affirmative nor negative ; every 
proposition is either affirmative or negative ; therefore, a 
problem is not a proposition. 

7. An enslaved people are not happy ; the English people 
are not enslaved ; therefore, the English are happy. 

8. None but whites are civilized ; the ancient Germans 
were whites ; therefore, they were civilized. 

9. If it is our duty now to love our neighbor, it was our 
duty to love him before he was born ; for the law of duty is 
unchangeable. 

10. Change is agreeable ; death is a change ; therefore, 
death is agreeable. 

11. Those who work hard deserve reward; those who 
work on the treadmill work hard ; therefore, they deserve 
reward. 

12. " No nation," says Earl Russell, in his speech in Par- 
liament, March 23d, 1865, " has a right to blockade one of 
its own ports when seized by insurgents, without recognizing 
such insurgents as belligerents ; " therefore, Irish insurgents 
seizing any port in Ireland have a right to open commerce or 
to be recognized as belligerents. 

13. No one who lives on terms of confidence with another 
has a right in any circumstances to take his life ; Brutus 
lived on terms of confidence with Caesar ; therefore, he had 
no right to take his life. 

14. He that destroys an usurper, does right ; Brutus 
destroyed an usurper ; therefore, he did right. 

15. None can perform impossibilities ; miracles are im- 
possibilities ; therefore, none can perform miracles. 

1 6. A story is not to be believed, the reporters of which 
give contradictory accounts ; the story of Bonaparte is con- 
tradictorily reported ; therefore, it ought not to be believed. 

17. That which requires self-denial is not habitual ; all 



EXERCISES IN REASONINGS. 219 

virtue requires self-denial ; therefore, no virtue can be hab- 
itual. 

18. Have you the ten marbles I gave you ? No ; I have 
not ten, for I have lost three. Have you lost all that you 
have not got ? Yes. Then you must have lost ten. 

19. Do you know what I am to ask? No. Then you do 
not know whether fish is fowl ; for that is what I was to ask. 

20. Do you know who that is in the street yonder ? No. 
Then you do not know your own father. 

21. Does one grain of corn make a heap ? No. Do two? 
No. Three? No. Nine hundred and ninety-nine? No. 
One thousand ? Yes. Then one grain makes the difference 
between a heap and no heap. 

22. Have you cast your horns? No. Then you must 
have them still. 

23. Can a body move where it is not ? No. Can a body 
move if it continue where it is ? No. Then a body cannot 
move at all, for it must move where it is or where it is not. 

24. Can a cause act except where it is ? No. Then how 
can the sun cause heat on the earth ? 

25. Every man is an animal ; a swan is not a man ; there- 
fore, no swan is an animal. 

26. No man is inanimate; snow is not man; therefore, 
snow is not inanimate. 

27. A horse may be white ; snow is not a horse ; there- 
fore, snow is not white. 

28. Honey is yellow ; gall is yellow ; therefore, gall is 
honey. 

29. He who is silent cannot speak ; John is silent ; there- 
fore, John cannot speak. 

30. The wise are good ; some ignorant people are good ; 
therefore, some ignorant people are wise. 

31. Animal food may be entirely dispensed with, for the 
Brahmins live without it ; and vegetable food may be dis- 
pensed with, for the Esquimaux live without it : but all 
food consists of animal food and vegetable food ; therefore, 
all food may be dispensed with. 



220 PURE LOGIC. 

32. In a perfect vacuum, nothing can be supposed to be ; 
therefore, in a perfect vacuum there can be no motion. 

33. No one desires evil, knowing it to be so ; to do wrong 
is evil ; therefore, no one desires to do wrong except in igno- 
rance. 

34. The action of living organism is vital action ; a fever 
is action of living organism ; therefore, a fever is vital 
-action. 

35. No trifling business will enrich those engaged in it; a 
mining speculation is no trifling business ; therefore, it will 
enrich whoever engages in it. 

36. He who is most hungry eats most; he who eats least 
is most hungry ; therefore, he who eats least eats most. 

37. He who calls you a man speaks truly ; he who calls 
you a poet calls you a man ; therefore, he who calls you a 
poet speaks truly. 

38. Nothing is heavier than platina ; feathers are heavier 
than nothing ; therefore, feathers are heavier than platina. 

39. All cold is to be expelled by heat ; this man's disorder 
is a cold ; therefore, it is to be expelled by heat. 

40. What w r e eat grew in the fields ; loaves of bread are 
what we eat ; therefore, loaves of bread grew in the field. 

41. We eat what we buy in the market; we buy in the 
market raw meat ; therefore, we eat raw meat. 

42. Jupiter is next to Mars ; Saturn is next to Jupiter ; 
therefore, Saturn is next to Mars. 

43. If Aristotle was infallible, Logic is worthy of being 
cultivated ; but Aristotle was not infallible ; therefore, Logic 
is unworthy of being cultivated. * 

44. If the Mosaic Law was designed only for Hebrews, 
the worship of images is not forbidden to Christians ; but it 
was not designed only for Hebrews ; therefore, the worship 
of images is forbidden to Christians. 

45. Every thing that exists, exists in space ; but space 
does not exist in space ; therefore, space does not exist. 

46. All rules have exceptions ; this very rule, itself, then, 



EXERCISES IN REASONINGS. 221 

that all rules have exceptions, has exceptions. It is not true 
then that all rules have exceptions. 

47. Let 9 be represented by x and 30 by y. Then if we 
take the self-evident equations ax s= ax and ay = ay, add 
them together, and transpose the terms, we shall have ax— 
ax=ay — ay. Dividing bja—a, we have x = y ; or 9 = 30. 

Exercise 14. Topics for discussion or investigation. 

1. History of the changes in meaning of the term Thought. 

2. What are the faculties of the intelligence ? 

3. Which are faculties of original cognition ? 

4. Diversity of opinion as to the proper sphere of Logic. 

5. The relationship of the true, the beautiful, and the 
good. 

6. How much of truth is there in the Hudibrastic 
couplet — 

" That all a Rhetorician's rules 
Serve only but to name his tools " ? 

7. Enumerate the intuitions of the mind. 

8. Classify the possible predicates in thought. 

9. The forms in which the subject of a sentence may be 
expressed in language. 

10. Enumerate the modals or modal adverbs in current 
use in the English language. 

11. Enumerate the general classes of concrete nouns in 
language. 

12. Enumerate the general classes of abstract nouns. 

13. What constitutes a species in the natural world ? 

14. What is the difference between reason and reasoning ? 

15. The meaning of the word Idea ; its etymological im- 
port, and the significance given it by Grecian, Roman, and 
modern philosophers. 

16. The meaning of the word Intuition, as determined by 
its etymology and use. 

17. The Nominalist controversy. 

18. The difference in meaning between substance and sub- 



& 



ject 



222 PURE LOGIC. 

19. The difference in meaning between truth and reality. 

20. The fundamental postulate in human belief. 

21. Belief and knowledge. 

22. Can a concept be imagined ? 

23. Example and induction. 

24. What is form ? 

25. Classification -of the sciences. 

26. The application of induction to moral matter. 

27. History of Logic. 

28. Indian Logic. 

29. Law and general fact. 

30. Law and idea. 

31. Identity and resemblance. 

32. Is all inference from particulars to particulars ? 

33. Is all deduction from a previous induction ? 

34. Comparison of the two methods of advancing science 
by observation : 1. By adding to the number of individuals 
or of species in the class ; 2. By adding to the attributes that 
belong to the class. 

35. Importance to success of consciously distinguishing the 
two methods of observation, stated above. 

36. Advancement of science by multiplication of classes, 
whether (1) by higher generalizations, or (2) by lower sub- 
divisions. 

37. Advancement of science by observation of attributes, 
whether (1) by discovery of new attributes, or (2) by anal- 
ysis of known attributes that are composite. 

38. Advancement of science by observation of attributes, 
whether (1) of properties, or (2) of relations. 



APPENDIX. 

*— 

A. 

INDUCTION. 

The proper nature and function of Induction as a process of 
Thought have been involved in much confusion and dispute, and, 
of course, in obscurity and error. To such extent is this true that 
Sir William Hamilton does not hesitate to declare in unqualified 
terms that all to be found in logical treatises on this subject " is 
utterly erroneous." Yet it is noticeable that with this disagree- 
ment there is still a harmony of view in regard to the leading 
characteristics of Induction, when they are regarded separately 
from the special theories held by the differing logicians ; which 
characteristics, thus separately admitted by all, or at least by the 
great majority, when brought together and wrought into system, 
make up a complete and altogether consistent and trustworthy 
doctrine of Induction. 

All agree in admitting Induction to be a process of Thought, and 
in regarding all Thought, as Thought, as properly within the pur- 
view of logical science. This admission at once disposes of the 
marvelous error of Hamilton in rejecting common, material Induc- 
tion, from the sphere of the Science of Thought. If this Induction 
is not a process of Thought, what is it indeed ? As well might he 
claim that engineering calculations do not come within the prov- 
ince of Arithmetical or of Geometrical Science. We can as well 
calculate in engineering without conforming to arithmetical and 
geometrical principles, as induce in Natural Science without con- 
forming to logical principles. 

Again, all agree in regarding Induction as a reasoning process. 
As a reasoning, it differs from a concept, inasmuch as the one ter- 
minates in a new judgment, while the other results in an object 



224 APPENDIX. 

t 

of thought which may be used as either subject or predicate in a 
new judgment ; but agrees with it in being a derivative process 
which gives a result not contained in the several given judgments 
from which the process starts as a datum, if they are taken sepa- 
rately. But it is a logical illusion to throw the result into the form 
of a Categorical Judgment instead of a Concept, in order to make 
it appear as an Induction. This disposes of the theory of those 
who confound Inductions with Concepts, and who exemplify this 
process thus : Socrates is rational, Plato is rational, Xenophon is 
rational ; Socrates, Plato, Xenophon are men ; therefore, men 
are rational. We have here a true method of forming a con- 
cept ; but we have no reasoning, only a fantasy ; for we have 
only substituted a single word for several expressing precisely the 
same object of thought. For evidently if we have attached any 
other meaning to men than what we mean by Socrates, Plato, 
Xenophon, either as to their Sphere or Extension, or as to their 
Comprehension, the whole process is a fallacy. It is equally illu- 
sive as it would be to say, Horse is four-footed ; equus is horse ; 
therefore, equus is four-footed, and suppose we have attained a 
new judgment respecting equus as an object of thought. This 
theory has soundness in it so far as it exemplifies a process of 
forming and naming concepts, but so far as designed to exemplify 
a reasoning, is merely a play upon words* 

Further, all agree in admitting a real distinction between In- 
ductive and Deductive Reasoning. This distinction they recog- 
nize as lying in the direction of the movement of the Thought — 
the one moving from the Whole as its starting-point, the other 
from the Part. They all accept the following as an example of 
true Inductive Reasoning : This, that, and the other magnet at- 
tract iron ; therefore, so do all. Now this admission should pre- 
clude the attempt to bring it under a deductive reasoning with a 
suppressed universal Major Premise or Sumption, as do Whately 
and others, or under a deductive reasoning with a suppressed 
Minor Premise or Subsumption, as does Aldrich. This is just to 
contradict their admission as well as to run counter to the teach- 
ing of their great authority, Aristotle, who expressly teaches that 
Induction is from the particular or individual, having apparently 
confounded the inductive process of Aristotle with what he calls 
the syllogism from induction. Aristotle's extant writings nowhere 
indicate that he viewed induction itself as syllogistic, and so ana- 



APPENDIX. 225 

lytic ; on the other hand, he ever opposes the one process to the 
other. 1 To suppose Induction to be an Enthymeme with Major 
Premise or Sumption suppressed, is entirely irreconcilable with 
such doctrine. This admission should preclude, also, any such 
fallacious attempt as that of Hamilton to make Induction a proc- 
ess from all the parts to the whole. This procedure is to be re- 
jected equally with that which we have already exposed as con- 
founding the mere substitution of one verbal expression for an- 
other with a new Judgment, and on the same ground. This will 
be seen at once from Hamilton's illustration : " This, that, and the 
other magnet attract iron; but this, that, and the other magnet, 
etc., are conceived to constitute the genus magnet; therefore, the 
genus magnet attracts iron" To say nothing of the irregularity 
in introducing in the Subsumption the very significant etc. into 
the middle term, it is clear that the Subsumption is a merely tau- 
tological proposition, and forms no part of the reasoning process. 
All the reasoning process has terminated when we have added the 
etc. There is the same fallacious substitution of a concept-form- 
ing process for a proper reasoning that has been already exposed. 
All agree in making the goal of the movement of Thought in 
Induction a conclusion which embraces in its subject the part 
complementary of that which formed the starting-point, as illus- 
trated in the example already given. This, that, and the other 
magnet attract iron ; therefore, all magnets attract iron. Of the 
class- whole magnet, this, that, and the other, forming the starting- 
point, are one part ; the conclusion evidently embraces with this 
the complement of the genus. But with this harmonious teach- 
ing so far, we find a great divergence of views in the further 
exposition of the result attained in an Induction. Hamilton 
and others, as has been shown, represent that the result is a 
simple gathering of the part given in the Major Premise with 
the complementary part into a concept; thus, The part observed of 
magnets attracts iron ; therefore, this part and the part unobserved 
make up the genus magnet. There is no proper reasoning in this ; 
it is simply a naming process disguised under the garb of a reason- 
ing. Others, as Whately, shun this error of Hamilton, but repre- 
sent the subject of the conclusion to be a genus, including, of 
course, both the datum and the complement. Others, as Thomp- 
son, in his " Laws of Thought," make the result of Induction " a 

1 See his Topics, 1. 10 ; Prior Analytics, II. 25 ; Rhetoric, I. 2. 
15 



226 APPENDIX. 

Law." But his Law is but the convertible term of General Fact, 
in the two different forms in which we apprehend Being. When, 
thus, we conceive of material bodies under the form of Substance, 
we say it is a General Fact that they are gravitating, — have this 
attribute ; when, on the other hand, we conceive of them under 
the form of Cause, we say it is the law of material bodies that 
they gravitate. Still another view is that which, through misinter- 
pretation of Aristotle, distinguishes Induction from Example as 
different processes of Thought — making one result in a genus, the 
other in a part as subject of the conclusion. But there is no es- 
sential difference in the movements of Thought ; they differ only 
in mere accidents of form and occasion. When from a given part 
we have induced to the complementary part, we have, in fact, 
comprehended the whole ; as, if P and C are the two parts which 
compose the whole W, then if what we know of P we have 
induced to be true of C, we have attained what is true of P and 
C, and accordingly of W, for W is but P and C taken together. 

Gathering up, now, the several teachings of logicians so far as 
they agree, we attain the following results as the accepted charac- 
teristics of Induction : — 

1. It is a process of Thought that is identical in essential char- 
acter in all those movements of Intelligence which induce, which 
infer mediately otherwise than by deduction. There is but one In- 
duction, as there is but one Deduction in all Thought. 

2. It is a reasoning, being a derivative Judgment, not a Con- 
cept ; an inference from a datum, implying a new proper Judg- 
ment-Cognition, not a mere synthesis of subjects or of predicates 
— that is, not a Concept. 

3. It is a mediate reasoning, being derived not from a single 
Judgment, but from a plurality of Judgments, related to each 
other under the relationship of part to complementary part in two 
of their terms which are alike related to the third or middle term 
as parts to a whole. 

Of the validity, independent character, and extensive use of 
this process of thought, the following extract from Mr. John Stu- 
art Mill's * Treatise on Logic " gives a very satisfactory illustra- 
tion : — 

" If, from our experience of John, Thomas, &c, who once were 
living, but are now dead, we are entitled to conclude that all 
human beings are mortal, we might, surely, without any logical 



APPENDIX. 227 

inconsequence, have concluded at once from those instances that 
the Duke of Wellington is mortal. The mortality of John, 
Thomas, and company, is, after all, the whole evidence we have 
for the mortality of the Duke of Wellington. Not one iota is 
added to the proof by interpolating a general proposition. . . . 
Not only may we reason from particulars to particulars without 
passing through generals, but we perpetually do so reason. All 
our earliest inferences are of this nature. From the first dawn 
of intelligence we draw inferences, but years elapse before we 
learn the use of general language. The child, who, having burnt 
his fingers, avoids to thrust them again into the fire, has reasoned 
or inferred, though he has never thought of the general maxim — 
' Fire burns.' He knows from memory that he has been burnt, 
and on this evidence believes, when he sees a candle, that if he 
puts his finger into the flame of it, he will be burnt again. He 
believes this in every case which happens to arise ; but without 
looking, in each instance, beyond the present case. He is not 
generalizing ; he is inferring a particular from particulars." Page 
125, New York Edition, 1860. 



B. 

ORIGIN OF LANGUAGE. 

In all speculations upon the Origin of Language, the two ele- 
ments in words, the thought-element — its significance, and the 
sound-element, should most obviously be kept entirely distinct. 
The thought-element must, further, be regarded as logically the 
antecedent, the occasioning, or prompting, and, so far at least, the 
determining element ; however true it may be that chronologically 
the two emerge simultaneously into conscious experience. How 
the thought-element originates and changes in the progress of 
thought and language, has been sufficiently indicated in the text, 
§ 85. The theory of Max Midler, as presented in the ninth of 
his First Series of Lectures on Language, that language origi- 
nates with general ideas, " that names," to use his own language, 
" are all, without exception, derived from general ideas," is there 
characterized as gross error. But in addition to the considerations 
there presented in justification of this unqualified rejection of the 



228 APPENDIX. 

theory, we may here present an exposition of the fallacy which viti- 
ates his whole reasoning. The fallacy lies in assuming that a predi- 
cate is essentially, and, of course, primitively a general idea. All 
nouns he teaches " express originally one out of the many attri- 
butes of a thing, and that attribute, whether it be a quality or an 
action, is necessarily a general idea." "All naming," he says, " is 
classification, bringing the individual under the general. ,, "Ana- 
lyze," he says again, " any word you like, and you will find that 
it expresses a general idea peculiar to the individual to which the 
name belongs. What is the meaning of moon ? The measurer. 
What is the meaning of sun ? The begetter. What is the mean- 
ing of earth ? The ploughed." And still again, " The fact that 
every word is originally a predicate, that names, though signs of 
individual conceptions, (?) are all, without exception, derived 
from general ideas, is one of the most important discoveries in the 
science of language." Now this assumption, so quietly and yet so 
confidently employed in this reasoning, is utterly baseless. A 
primitive predicate must have been an individual property. A 
generic notion is a purely artificial notion — a mere product of 
thought — a creation of thinking man. It could not exist before 
man thought ; and as his first thought was a judgment, a recogni- 
tion of an attribute as belonging to an object, that attribute could 
not have been a genus, that is, a thought-product. The learned 
lecturer has undoubtedly confounded the actual with the potential, 
the simple germinant with the complicated mature. Because moon 
means measurer, which is assumed in the argument to be a primi- 
tive predicate, he assumes that it was so named because measurer 
at that primitive time of naming, was generic — included a class 
of objects as then known in human speech, for he is emphatic in 
his teaching that thought and speech originate together — "lan- 
guage and thought are inseparable." But all this is error. Meas- 
urer was not actually generic, but only potentially so ; that is, the 
simple attribute of measurer, assuming it still to be a primitive 
word, originally applied to an individual object — say the moon, 
and to that only, was only afterwards, in the progress of thought 
and speech, applied to other objects, as one after another they 
came into human consciousness. Only in this way did it come to 
be generic. It could not have been generic, at first, in the possi- 
bilities of human experience ; it became so. In other words, it 
was not actually, but only potentially generic. This fundamental 



APPENDIX. 229 

fallacy vitiates his whole reasoning, and involves it in absurdities 
all along his path. His illustrations to prove the origin of words 
never go back to a first, but only to a prior, which must itself have 
had a prior. Cave was named from the idea to cover. But whence 
did cover originate ? Was it primitive ? Then it must have ex- 
isted before its class, and, of course, could not have been at that 
time generic. Yet it is the origin of words, the rise of the first 
words, that the theory attempts to explain. So " all naming," he 
says, " is classification, bringing the individual under the general." 
How then could the first naming have been effected ? Was the 
general before the individual which it includes ? As " language 
and thought are inseparable," this general that is antecedent to 
all naming, that is, to all language, must have been before all 
thought. When and what was it ? 

The question as to the origin of the sound-element in the word, 
how a particular sound comes to embody a notion, what deter- 
mines this and that sound to this and that idea, is a totally distinct 
question. M. Miiller in his lectures mentions three theories. One 
is, that the roots of words are imitations of sounds ; a second, that 
they are involuntary interjections. These two theories he rejects, 
and styles them respectively the Bow-wow theory, and the Pooh- 
pooh theory. The third is his own. These original phonetic 
roots in language are "phonetic types produced by a power in- 
herent in human nature." " There is a law which runs through 
nearly the whole of nature, that every thing which is struck rings. 
Each substance has its peculiar ring." Man in his primitive state 
possessed a faculty that has now become extinct, since its object is 
fulfilled, " by which every impression from without received its 
vocal expression from within." By this faculty man created these 
phonetic types to an almost infinite extent at the beginning, but 
by a process of elimination reduced them ere long to some four or 
five hundred. This theory assumes this strange fact of a primitive 
faculty now extinct, without a shadow of warrant, except the 
necessities of the theory. It is, moreover, as unintelligible as it is 
baseless. 

We must take the fact that man is capable of embodying his 
cognitions in vocal sounds, and is pressed by an irrepressible . in- 
stinct to give such vocal expression to his thoughts, as an ultimate 
fact. Why he selects this and not that out of the multiplicity of 
vocal sounds to embody a given thought, is a question that can 



230 APPENDIX. 

only be answered generally, that the selection is determined by 
some accidental association at the time of forming the word, that 
is, by some identification of the thought with the particular sound 
in its nature, its condition, or relation. The object named may be 
a sound, and the name may resemble that. It may be one that 
utters or makes a sound, and the name may be taken from re- 
semblance to that. It may make an impression that shall occa- 
sion an exclamation, or that shall be similar in some respect to 
that made by another object already named, and be named accord- 
ingly. It may be associated with some sound from other objects 
at the time, or it may be associated with some other words already 
formed ; or still other associations may exist, and so the particular 
name be determined as to its sound. 

As language may reasonably be supposed to have originated in 
the desire to communicate, and not in the mere impulse to embody 
a mental state in sound, we may suppose that the first words were 
sounds which would be regarded by the first speaker as associated 
in some way with the mental state to be communicated as well by 
the person addressed as by himself. This mental state may have 
been a sight of some object visible to both, or of some sound audi- 
ble to both, and the sound adopted to express it may have been 
either determined by some common experience of a sound-sensa- 
tion, or arbitrarily connected with it by some demonstrative act 
on the part of the speaker. Or this mental state, to be communi- 
cated in the primitive word, may have been that of a sensation 
through some other sense, or through the general sensual organ- 
ism. What more natural than to suppose that a sensation of cold 
may have prompted such primitive word, the sounds in which may 
have been such as would naturally express shuddering, as the He- 
brew root Kar — cold ? What may be thus supposed in regard 
to the first word actually spoken by man, may be supposed with 
like reason in regard to all proper primitives, or root-words. Thus 
we may imagine to ourselves how words in the progress of speech 
came successively into being in the instinctive desire in man to 
communicate his own experiences to his fellow, which desire he 
could gratify only through sensations common to both speaker and 
hearer, these sensations being identified by some determination of 
place or time, and being as various as the possible sensations of 
which man is susceptible, that can thus be identified by different 
persons. It is idle to argue in favor of any one sense or any one 



APPENDIX. 231 

sensation, as furnishing the occasion for the production of the prim- 
itive word. It is worse to found a theory of language, as some 
able grammarians have done, upon the groundless assumption that 
the primitive thought, the first experienced or communicated, was 
a sight — as a motion, an activity, predicated of some object. 



INDEX. 



A. 

Abstraction, 33. 

^Esthetic whole, 28. 

Affirmative judgment, 48. 

Amplification of concepts, 73. 

Analysis, 33 ; as a process of attain- 
ing distinctness, 173. 

Antecedent of a reasoning, 93. 

Apodictic judgment, 51. 

Argumentation, 92. 

Assertory judgment, 51. 

Attention, 34. 

Attributes, their various denomina- 
tions, 19, 20. 

Axioms, 61. 



B. 



Base of a concept, 63. 

Begging the question, fallacy of, 191. 



Categorical judgment, 53. 

Categorical syllogism, 103 ; two 
kinds, deductive and inductive, 
105; its subjective law, 190. 

Causal analvsis, 174; how perform- 
ed, 179; its law, 179. 

Causal judgment, 58; rules of, 155. 

Causal whole, 27, 28. 

Chain of reasoning, 128. 

Characters, a designation of attri- 
butes, 20. 

Circle, fallacy of, 192. 

Classification, 80. -* 

Clearness a virtue in the formal per- 
fection of science, 136 ; attained by 
definition, 104. 



Co extension in concepts, 78. 

Collective whole, 27. 

Comparison, 34. 

Completeness, law of, 174. 

Composition, a variety of immediate 
reasonings, 102. 

Composition and Division, fallacv of, 
191. 

Comprehensive judgment, 56; rules 
of, 155. 

Comprehensive quantity of a con- 
cept, 73. 

Comprehensive whole, 28. 

Concept, formation, 62 ; definition, 
63 ; under law of Identity, 63 ; a 
relative and one-sided cognition, 
64 ; not a reality, 65 ; how to be 
realized, 66; a quantity, 72; am- 
plification, 73 ; relations of in ex- 
clusion, co extension, subordina- 
tion, coordination, intersection, 
78 ; identical and different, 86 ; 
opposition, congruent and conflict- 
ive, 87; intrinsic and extrinsic, 
89 ; methodology, 157 ; threefold 
perfection, 157 ; objective law, 157 ; 
correspondence with realities, 160- 
162; subjective law, 163; verbal 
law, 181. 

Concept words, their genesis, 139- 
144. 

Concretion, 75. 

Conditional syllogism, 118 ; two 
modes, ponent and tollent, 119; 
distinguished in respect to quan- 
tity into hypothetical and disjunct- 
ive, 120. 

Congruence, a virtue in the formal 
perfection of science, 138. 

Consequent, a part of a reasoning, 
93. 



234 



INDEX. 



Consequents, a designation .of attri- 
butes, 20. 

Conspeeies, 85. 

Contradiction, law of, 24. 

Conversion, 96; its subjective law, 
187. 

Coordination of notions extensive, 
78 ; intensive, 89. 

Copula of a judgment, 38. 

Corporate whole, 29. 

Correctness, a virtue in the verbal * 
perfection of science, 144. 

Correspondence between thought 
and reality, 162. 

D. 

Deductive syllogism, 105 ; two kinds, 
extensive and comprehensive, 109 ; 
its subjective law, 190. 

Definition, the process for attaining 
clearness, 164 : import of, 161 ; its 
kinds, 168 ; verbal, real, and genet- 
ic, 169. 

Definitives, 141. 

Demonstrable propositions, 60. 

Determination of concepts, 74. 

Determinations, a designation of at- 
tributes, 20. 

Dianoetic whole, 27. 

Differences, a designation of attri- 
butes, 20. 

Dilemma, a kind of judgment, 55; 
a kind of syllogism, 122 ; its sub- 
jective law, 204. 

Discourse, 92. 

Discrete, or disjunct notions, 85. 

Disjunction, law of, 24; a variety 
of immediate reasonings, 102. 

Disjunctive judgment, 48; its three 
forms, 48; rules of, 149, 150. 

Disjunctive syllogism, 125; ponent 
and tollent modes, 126 ; its subject- 
ive law, 203. 

Dissection, a process of logical anal- 
ysis, 173 ; its two kinds, special 
and numerical, 175. 

Distinctness, a virtue in the verbal 
perfection of science, 138 ; attained 
by analysis, 164 ; its conditions, 
173; its law, 173. 

Division, a process of logical analysis, 
. 174; how performed, 176; its law, 
177, 178. 

Elements of thought, laws and prod- 
ucts, 17. 



Enthymeme, 94. 

Epichirema, 129. 

Epithets, 141. 

Essential whole, 27. 

Evolution, or causal analysis, 174 ; 
how performed, 179 ; its law, 179. 

Exclusion, law of, 25 ; relation of in 
concepts, 78. 

Exercises in judgments, 207; in con- 
cepts, 214 ; in reasonings, 214. 

Experimental propositions, 61. 

Extensive deductive syllogism, 109- 
111. 

Extensive judgment, 56 ; rules of, 
155. 

Extensive quantity of a concept, 73. 

Extensive whole, 28. 

F. 

Fallacies to be detected, 217. 

Fallacy of composition and division, 
191 ; of unreal universality, 191 ; 
petitio principii, 191; hysteron pro- 
ieron, 192 ; .of the circle, 192 ; saltus, 
192; ignava ratio, 193; non causa 
pro causa, or post hoc ergo propter 
hoc, 195. 

Formal perfection of science, 137; 
its three virtues — clearness, con- 
gruence, distinctness, 138. 

Formal whole, 29. 

G. 

Generalization, 74, 80. 
Generic difference, 84. 
Genus, 82 ; of two degrees, 83. 
Geometrical whole, 27. 



H. 

Heterogeneity, law of, 86. 
Hindoo system of reasoning, 107. 
Homogeneity, law of, 86. 
Hypothesis, 61. 
Hypothetical judgment, 54; rules of, 

153. 
Hypothetical syllogism, 120; two 

modes, ponent and tollent, 120 ; two 

varieties — proper hypothetical and 

dilemma, 122; its subjective law, 

202. 
H vpothetico - disj unctive j udgment, 

*55. 
Hy pothetico - disj unctive syllogism, 

122; subjective law, 204. 
Hysteron proteron, fallacy of, 192. 



INDEX. 



235 



I. 

Identical judgment, 53. 

Identical notions, 86. 

Identity, law of, 24. 

Jqnava ratio, fallacy of, 193. 

Illation, 92. 

Immediate reasoning, 93, 94. 

Indemonstrable propositions, 60. 

Individual difference, 84. 

Induction, its nature, 223. 

Inductive syllogism, 112-118; its 

subjective law, 195. 
Inference, 92. 
Integrate judgment, 57/, rules of, 

155. 
Integrate whole, 27. 
Intensive deductive syllogism, 109- 

Intensive judgment, 56 ; rules of, 155. 
Intensive quantity of a concept, 73. 
Intensive whole, 28. 
Investigation and probation distin- 
guished, 183. 
Involution of concepts, 89. 



Judgment defined, 31; parts, 35; 
division, 39-47 ; judgments in re- 
lation to one another, 58 ; method- 
ology, 147 ; three conditions of 
perfection in judgments, material, 
formal, and verbal, 147 ; rules of a 
perfect judgment, 148, 155, 156. 



Language, its relation to thought, 
69, 138-144; its origin, 227. 

Laws of thought, four in number, 21 ; 
how evolved, 21 -24 ; of identity, 
24 ; of contradiction, 24 ; of dis- 
junction, 24 ; of exclusion, 25 ; 
subjective and objective laws, 25. 

Lemmata, 61. 

Logic defined, 1 ; whether an art or 
a science, 1 ; its object matter, 
thought, 2; its objective utility as 
science of thought, 3 ; as pure 
science, 4; its subjective utility as 
aid to discovery, 6; as builder of 
science, 6 ; as corrective of error, 
9; as assuring truth, 9; as invig- 



orating the understanding, 10 ; as 
affording a nomenclature, 10 ; its 
divisions, objective and subjective, 
12 ; abstract and concrete, 12 ; pure 
and modified, 15 ; parts of pure 
logic — doctrine of elements and 
doctrine of method, 16. 

Logical definition, 169, 

Logical quadruped, fallacy of, 190, 
191. 

Logical whole, its two species, ex- 
tensive and intensive or compre- 
hensive, 28. 



M. 

Major premise, 107. 

Major term in a syllogism, 106. 

Marks, a designation of attributes, 
20. 

Mass whole, 27. 

Material perfection of science, 136 ; 
its two virtues, adequateness and 
accuracy, 137. 

Mathematical whole — numerical 
and spacial, 27. 

Mediate reasoning, 94 ; of two class- 
es, 102. 

Method what, 132 ; its different ends, 
132. 

Methodology, 132 ; its divisions, 145 ; 
of judgments, 147 ; of concepts, 
157; of reasonings, 183. 

Middle term in a syllogism, 106. 

Minor premise, 107. 

Minor term in a syllogism, 106. 

Modal judgments, rules of, 51. 

Modal restriction, a variety of imme- 
diate reasonings, 98; its subjective 
law, 188. 

Modality of a judgment, 40. 

Modes of cogitable matter denoted 
by various terms, 19. 

Monosyllogism, 128. 



N. 



Necessary judgment, 51. 

Negative judgment, 48 ; rules of, 

149. 
Non causa pro causa, fallacy of, 195. 
Notes, a designation of attributes, 

20, 
Numerical difference, 84. 
Numerical whole, 27. 



236 



INDEX. 



o. 

Objective law of a judgment, 148; 
of a concept, 157 ; of a reasoning, 
184. 

Opposition in logic, 48 ; contradic- 
tory, 49, 88; contrary, 49, 88. 



Partial judgment, 53; rules of, 

152. 
Particular notions, 80. 
Partition, a process of logical anal- 
ysis, 174; how performed, 178; its 

law, 178, 179. 
Perspicuousness, a virtue in the 

verbal perfection of science, 144; 

its subordinate qualities, 145. 
Petitio principii, fallacy of, 191. 
Polylemma, 123. 
Polvsyllogism, 94, 128 ; two kinds, 

Epichirema and Sorites, 129; 

mode of verifying, 205. 
Ponent mode "of the conditional 

syllogism, 119. 
Post hoc ergo propter hoc, fallacy of, 

195. 
Postulate of logic, 29. 
Postulates, 61. 
Practical propositions, 60. 
Praxis, 207. 
Predicables, predicates, predicaments, 

designations of attributes, or modes 

of being, 20. 
Predicate of a proposition, 35. 
Principle of division, 176. 
Probation and investigation distin- 
guished, 183. 
Problematic judgment, 51. 
Problems, 60. 
Products of thought, 31. 
Progressive syllogism, 129. 
Properties, designations of attributes, 

20. 
Proposition, 31. 
Pure logic, its divisions, 16. 



Q- 

Qualities, their various denomina- 
tions, 19. 

Quantitative restriction, 97; its sub- 
jective law, 188. 

Quantity, relation of, in all thought, 
25; of concepts, extensive and 



intensive, 72 ; these quantities 
how opposed to each other, 77. 



R 



Ratiocination, 92. 

Reasoning, denned, 91; how denom- 
inated, 92; its parts, 93; immedi- 
ate reasonings, 93; mediate, 94; 
methodology of reasonings, 183; 
objective law, 184; subjective law, 
185 ; complex reasonings to be 
resolved for separate verification 
of parts, 185-187. 

Regressive syllogism, 129. 

Representative whole, 29. 

Resolution, a process of logical anal- 
ysis, 194 ; how performed, 179 ; 
its law, 179. 



Saltus, fallacy of, 192. 

Scholia, 61. 

Science, its threefold perfection — 

material, formal, and verbal, 133. 
Sentence, 31. 
Signs, a designation of attributes, 

20. 
Sorites, 94, 130. 
Spacial whole, 27. 
Species, 80 ; of two degrees, 83. 
Specific difference, 84. 
Specification, 80, 82. 
Subject of a proposition, 35. 
Subjective law of a judgment, 148; 

of a concept, 164 ; of a reasoning, 

185. 
Subordination of notions, 78, 79. 
Substantial judgment, 57 ; rules of, 

155. 
Substantial whole, 27. 
Subsumption, 108. 
Sumption, 107. 

Syllogism, 92, 93; single, 94; poly- 
syllogism, 94 ; categorical and 

conditional, 94. 
Synthesis, 34. 



Tautological judgment, 53. 

Terms of a judgment, 35-38; three 

gradations, 37 ; in a syllogism, 

106. 



INDEX. 



237 



Theorems, 61. 

Theoretical propositions, 60. 

Thought, the object matter of logic, 
2; its narrower import as product 
of the discursive faculty, 2; its 
essential nature, 17 ; a relative 
cognition, or a cognition of a du- 
ality of cognitions, 17; its four 
fundamental laws, 21 ; its products, 
31; its relations to its matter, 
136. 

Tollent mode of the conditional syl- 
logism, 119. 

Topics for discussion or investiga- 
tion, 221. 

Transference, a variety of immediate 
reasoning, 98 ; its two kinds, as 
qualitative and modal, 101 ; its 
law, 189. 

Trilemma, 123, 



U. 

Universal notions, 80. 

Unreal universality, fallacy of, 191. 

Utility of logic, 2. 



v. 



Verbal law of a judgment, 148; of a 

concept, 181. 
Verbal perfection of science, 138 ; its 

two virtues, correctness and per- 

spicuousness, 144. 



w. 

Wholes in thought enumerated, 27; 
j>er se, 27 ; j?er acciden$, 29. 



THE END. 



Deacidified using the Bookkeeper process 

Neutralizing agent: Magnesium Oxide . 
Treatment Date: Sept. 2004 

PreservationTechnologies 

A WORLD LEADER IN PAPER PRESERVATION 

1 1 1 Thomson Park Drive 
Cranberry Township, PA 16066 
(724)779-2111 



